is this c/10 spaceship known?

[Apple Bottom]

Would anyone have actually explored D2_+2 to this extent if it weren't for zdr's prior discovery of the copperhead?

Well, I for my part can say I was blissfully unaware that this symmetry might be especially prone to producing a copperhead, or indeed anything of particular interest.

[gmc_nxtman]

Copperhead to glider, repeat time 564:

Code: Select all

x = 63, y = 94, rule = LifeHistory
6.A2.A$6.A2BA$6.B2AB$5.6B$5.6B$4.2A4B2A$3.2BA4BA2B$3.4B2A4B$3.2BAB2AB
A2B$3.2B2A2B2A2B$3.2B2A2B2A2B$3.3BA2BA3B$3.4B2A4B$3.10B$3.10B$3.10B$
3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.
10B$3.10B23.2A$3.10B22.A.A$3.10B16.2A4.A$3.10B14.A2.A2.2A.4A$3.10B14.
2A.A.A.A.A2.A$3.10B17.A.ABABAB$3.10B17.A.AB2AB$3.10B18.AB.2B$3.10B21.
3B$3.10B21.4B6.2A$3.10B19.3B2AB6.A$3.10B19.3B2AB3.BA.A$3.10B17.10B.B
2A$3.10B16.13B$3.10B15.14B$3.10B14.15B$3.10B13.4B2.8B$3.10B12.4B5.6B$
3.10B11.4B4.9B$3.10B10.4B5.2A4.4B$3.10B9.4B7.A5.4B$3.10B8.4B5.3A7.4B$
3.10B7.4B6.A10.4B$3.10B6.4B19.4B$3.10B5.4B21.4B$3.10B4.4B23.4B$3.10B
3.4B25.4B$3.10B2.4B27.4B$3.10B.4B29.4B$3.4B2A8B31.4B$3.4B2A7B33.4B$3.
12B35.4B$3.11B36.4B$3.2BA4BA2B37.5B$3.BAB4ABAB3.B32.9B$4.3A2B3A2B.B2A
31.9B$4.BA4BA5B2A31.9B$4.BA4BA4B.B31.10B$4.BA4BA3B33.12B$5.A4BA4B22.
2A8.13B$5.BA2BA6B22.A9.11B$5.BA2BA2B.4B21.A.AB4.12B$4.2B4.B3.4B10.A
10.2AB.15B$4.2AB8.4B7.3A12.17B$2A.A.A10.4B5.A15.17B$A.2A.A.A9.4B4.2A
15.17B.B$6.2A2.2A6.9B14.19B2A$11.A7.6B14.19B.B2A$11.A.2A5.6B3.B2.2B2.
20B4.B$12.A2.A4.36B$13.2AB3.27B.9B$14.14B2A16B2.7B$15.13B2A16B2.7B$
16.29B4.6B$16.17B.B.2B10.7B$17.15B4.3B10.6B$17.15B5.A2B.2A6.7B$18.13B
5.A.A2B.A7.5B$20.13B2.A.AB2.A8.6B$19.8B4.2A.A.A3.A7.9B$19.6B6.2ABA2.
4A.A5.2A.7B$19.5B8.B2.A.A3.A.A5.A5.4B$19.B.B9.2A.2A2.A2.A.A2.3A7.4B$
20.3B9.A.A2.2A3.A3.A10.4B$19.B2AB9.A.A23.4B$20.2A11.A25.4B!

EDIT: Repeat time 546:

Code: Select all

x = 97, y = 92, rule = LifeHistory
6.B2AB$6.A2BA$5.A4BA$5.6B$4.A6BA$4.B2A2B2AB$3.10B$3.3BA2BA3B$3.2BAB2A
BA2B$3.3B4A3B$3.3BA2BA3B$3.4B2A4B$3.4B2A4B$3.10B$3.10B$3.10B$3.10B$3.
10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B$3.10B
$3.10B$3.10B$3.10B$3.10B17.2A$3.10B16.A.A$3.10B10.2A4.A$3.10B8.A2.A2.
2A.4A$3.10B8.2A.A.A.A.A2.A$3.10B11.A.ABABAB$3.10B11.A.AB2AB$3.10B12.A
B.2B$3.10B15.3B$3.10B15.4B6.2A$3.10B13.3B2AB6.A$3.10B13.3B2AB3.BA.A$
3.10B11.10B.B2A$3.10B10.13B$3.10B9.14B$3.10B8.15B$3.10B7.4B2.8B$3.10B
6.4B5.6B$3.10B5.4B4.9B32.2A$3.10B4.4B5.2A4.4B30.B2AB$3.10B3.4B7.A5.4B
30.3B$3.10B2.4B5.3A7.4B16.2A12.B$3.10B.4B6.A10.4B16.A6.B4.3B$3.4B2A8B
19.4B15.A.AB.5B.5B$3.4B2A7B21.4B15.2AB.11B$3.12B23.4B16.14B$3.11B25.
4B15.14B$3.2BA4BA2B27.4B7.2A5.14B$3.BAB4ABAB3.B24.4B5.B2AB5.13B$4.3A
2B3A2B.B2A24.4B5.3B5.13B$4.BA4BA5B2A25.4B3.B.B6.12B$4.BA4BA4B.B27.4B.
6B5.13B$4.BA4BA3B31.10B4.15B$5.A4BA4B22.2A7.28B$5.BA2BA6B22.A8.28B$5.
BA2BA2B.4B21.A.AB6.27B3.2A$4.2B4.B3.4B10.A10.2AB.3B2.28B3.A$4.2AB8.4B
7.3A12.36B2.A.AB$3.A.A10.4B5.A15.36B3.A.AB.B$.3A.A.A9.4B4.2A15.34B5.A
3B2A$A5.2A2.2A6.9B14.33B6.3B.B2A$2A9.A7.6B14.31B10.2B3.B$11.A.2A5.6B
3.B2.2B2.20B3.12B.2B.3B.4B$12.A2.A4.35B5.30B2.B$13.2AB3.27B.7B6.13B2A
11BD7B$14.14B2A16B2.6B7.12B2A9B3D7B$15.13B2A16B3.6B8.21BDBD9B$16.29B
6.4B6.23BD11B$16.17B.B.2B12.B2A2B6.2A.11B2.2B2.14BAB$17.15B4.3B12.2A.
B2A5.A2.9B10.10BABA$17.15B5.A2B.2A11.BA.A.3A3.9B12.8BABA$18.13B5.A.A
2B.A14.A.A4.8B15.8BA$20.13B2.A.AB2.A15.2A4.2AB.4B15.10B$19.8B4.2A.A.A
3.A21.A.AB.2B2AB14.9B$19.6B6.2ABA2.4A.A19.A6.2A15.8B$19.5B8.B2.A.A3.A
.A17.2A24.7B$19.B.B9.2A.2A2.A2.A.A44.5B$20.3B9.A.A2.2A3.A46.2B$19.B2A
B9.A.A$20.2A11.A!

[thunk]

Copperhead to glider, repeat time 564:

Rearranged, for repeat time 524 (may be a few ticks less):

Code: Select all

x = 91, y = 116, rule = LifeHistory
4$28.B2.B6$28.B2AB$28.B2AB$27.6B$27.6B$26.ABA2BABA$25.BAB4ABAB$25.BA
2B2A2BAB$25.10B$25.10B$25.2B6A2B$25.3BA2BA3B$25.3B4A3B$25.10B$25.10B$
25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B
$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.10B$25.
10B25.2A16.2B$25.10B24.B2AB14.3B$25.10B18.B6.2B14.4B$25.10B17.3B4.2B
14.4B$25.10B13.14B12.4B$25.10B13.14B11.4B$25.10B13.17B5.B.4B$25.10B
12.28B$25.10B10.30B$25.10B9.31B$25.10B8.32B$25.10B7.32B$25.10B6.4B3.
23B2.B2A$25.10B5.4B7.16B.B4.BA.A$25.10B4.4B9.2B.10B11.A$25.10B3.4B13.
9B12.2A$25.10B2.4B15.11B$25.10B.4B16.12B$25.4B2A8B17.12B7.2A$25.4B2A
7B19.11B2.2A2.A2.A$25.12B18.4B.8B2.A.A2.2A$25.3B4A4B19.2A4.7B3.B.2A$
25.2B2A2B2A2B21.A4.7B2.2B2.A$25.BA6BAB3.B14.3A6.6B.2BAB.A.2A$26.10B.B
2A13.A8.8BA.A.2A.A$26.A6BA4B2A22.8B.A.A$26.ABA2BABA3B.B24.5B4.A2.2A$
26.3B2A5B27.6B4.2A.3A$27.2B2A6B25.6B6.B4.A$27.2A2B2A5B16.2A6.7B3.B2AB
3A$27.2A5B.4B15.A2.A5.8B.B2A.A$26.2A4.B3.4B15.3A5.10B$26.B2A8.4B21.3B
2A6B$22.2A.A.A10.4B13.3A5.2B2A6B$22.A.2A.A.A9.4B11.A2.A5.10B$28.2A10.
4B10.2A.A.AB2.11B$41.4B11.A.2AB.12B$42.4B10.A3.15B$43.4B7.3A3.16B$44.
4B5.A6.16B.2B$45.4B4.2A5.18B2A$46.9B4.17B.B2A$47.6B5.4B2.8B.4B.B$47.
8B2.4B4.7B$45.15B5.6B$45.14B6.4B$45.13B5.A3B$43.2AB.10B5.A.AB$42.A.AB
3.B2A3B7.A.A$42.A6.B2A3B8.A$41.2A6.4B7.3A$50.3B3.B3.A$51.2B.BA$50.B2A
BA.A$49.BABABA.A$47.A2.A.A.A.A.2A$47.4A.2A2.A2.A$51.A4.2A$49.A.A$49.
2A!

[Scorbie]

I'm pretty sure there's a better initiating reaction, possibly with baits. I really wish I had time for this...
@Kazyan I think you did search for copperhead ptbs with Bellman... Are there any other ones?

[chris_c]

More tweaking to get down to 495 ticks:

Code: Select all

x = 49, y = 99, rule = LifeHistory
3.10B$3.10B$3.10B$3.10B$3.4B2A4B$3.3B4A3B$3.10B$3.10B$3.2BA4BA2B$3.2B
A4BA2B$3.2B2A2B2A2B$3.3B4A3B$3.2BA4BA2B35.B$3.2BA4BA2B34.2B$3.3BA2BA
3B33.3B$3.3BA2BA3B32.4B$3.4B2A4B31.4B$3.10B30.4B$3.10B29.4B$3.10B28.
4B$3.10B27.4B$3.10B26.4B$3.10B25.4B$3.10B24.4B$3.10B23.4B$3.10B22.4B$
3.10B21.4B$3.10B9.A10.4B$3.10B9.3A7.4B$3.10B12.A5.4B$3.10B11.2A4.4B$
3.10B11.9B$3.10B13.6B4.A$3.10B12.7B3.A.A$3.10B11.8B.A2.A.A$3.10B9.B.
9B2A.A.A$3.10B8.2A9B2.B.2A$3.10B8.2A10B2A$3.10B9.10BA2.3A$3.10B9.8B.
2B2A3.A$3.10B11.6B4.A2.A$3.10B11.7B3.A.A$3.10B10.8B4.A5.A$3.10B9.9B8.
3A$3.10B9.9B7.A$3.10B9.10B6.2A$3.10B7.13B2.5B$3.10B4.2B.18B$3.10B3.2A
19B2A$3.10B3.2AB.17B2A$3.10B4.B.17B.B$3.10B7.16B7.2A$3.10B8.14B8.A.A$
3.10B7.4B2.8B11.A$3.4B2A4B6.4B3.7B12.2A$3.4B2A4B5.4B3.11B$3.10B4.4B4.
12B$3.10B3.4B5.12B7.2A$3.2BA4BA2B2.4B7.11B2.2A2.A2.A$3.BAB4ABAB.4B6.
4B.8B2.A.A2.2A$3.B3A2B3A5B7.2A4.7B3.B.2A$3.2BA4BA5B9.A4.7B2.2B2.A$3.
2BA4BA4B7.3A6.6B.2BAB.A.2A$3.2BA4BA3B8.A8.8BA.A.2A.A$3.2BA4BA2B18.8B.
A.A$3.3BA2BA3B19.5B4.A2.2A$3.3BA2BA3B19.6B4.2A.3A$3.10B18.6B6.B4.A$3.
10B18.7B3.B2AB3A$3.10B19.8B.B2A.A$3.10B19.10B$3.10B3.B14.3B2A6B$4.10B
.B2A7.2A5.2B2A6B$4.12B2A5.A2.A5.10B$4.11B.B6.2A.A.AB2.11B$4.10B11.A.
2AB.12B$5.10B10.A3.15B$5.6B.4B7.3A3.16B$5.5B3.4B5.A6.16B.2B$4.2B8.4B
4.2A5.18B2A$4.2AB8.9B4.17B.B2A$2A.A.A10.6B5.4B2.8B.4B.B$A.2A.A.A8.8B
2.4B4.7B$6.2A6.15B5.6B$14.14B6.4B$14.13B5.A3B$12.2AB.10B5.A.AB$11.A.A
B3.B2A3B7.A.A$11.A6.B2A3B8.A$10.2A6.4B7.3A$19.3B7.A$20.2B.BA$19.B2ABA
.A$18.BABABA.A$16.A2.A.A.A.A.2A$16.4A.2A2.A2.A$20.A4.2A$18.A.A$18.2A!

[Kazyan]

I'm pretty sure there's a better initiating reaction, possibly with baits. I really wish I had time for this...
@Kazyan I think you did search for copperhead ptbs with Bellman... Are there any other ones?

I hadn't done any Bellman searches on a Copperhead, but hopefully it'll return something good tomorrow morning after I run it overnight.

[simeks]

Copperhead-with-tagalong to glider, repeat time 325:

Code: Select all

x = 28, y = 61, rule = LifeHistory
20.2C$14.2C5.C$14.C.C.3C$16.C.C$16.2C4$13.2A$12.A2.A$12.A2.A$11.A4.A$
11.A4.A$2C10.4A$.C2.C6.2A2.2A$.C.C.C5.A4.A$2C.2C6.A4.A9.2C$26.C$2C.2C
19.C.C$.C.C8.4A8.2C$.C.C9.2A$2.C$10.2A4.2A$9.A2.A2.A2.A$10.3A2.3A5.2C
$10.2A4.2A5.C$24.3C$26.C13$12.A2.A$12.A2.A$11.A4.A$11.A4.A$11.A4.A$
11.A4.A$10.3A2.3A$10.A.4A.A$11.A4.A3$13.2A$13.2A$13.2A$11.A4.A$9.3A4.
3A$8.3A6.3A$8.2A8.2A$9.10A$10.8A$12.4A!

EDIT: And to B/H:

Code: Select all

x = 36, y = 119, rule = LifeHistory
20.2C$14.2C5.C$14.C.C.3C$16.C.C$16.2C4$13.2A$12.A2.A$12.A2.A$11.A4.A
9.C$11.A4.A7.3C$2C10.4A7.C$.C2.C6.2A2.2A6.2C$.C.C.C5.A4.A12.C$2C.2C6.
A4.A10.3C$26.C$2C.2C21.2C$.C.C8.4A$.C.C9.2A$2.C$10.2A4.2A$9.A2.A2.A2.
A$10.3A2.3A$10.2A4.2A$30.2C$29.C.C$30.C7$32.2C.C$32.C.2C2$25.2C$25.2C
14$35.E$33.3E$32.E$32.2E9$27.2E$27.E2.E$28.2E.E$31.E$26.E4.E.2E$24.3E
3.2E.2E$23.E$23.2E29$13.2A$11.2A2.2A$13.2A$10.A6.A$11.A4.A$13.2A$10.
3A2.3A$10.2A4.2A3$13.2A$12.A2.A2$11.A4.A$10.2A4.2A$9.A2.A2.A2.A$9.2A.
4A.2A$11.A4.A!

[muzik]

Is there any way to shave the tagalong off and turn it into a normal copperhead?

[towerator]

Is there any way to shave the tagalong off and turn it into a normal copperhead?

This works:

Code: Select all

x = 14, y = 34, rule = B3/S23
6b2o$6b2o$5bo2bo$5b4o$4bob2obo$5bo2bo2$4b2o2b2o$3bo6bo2$4bo4bo$5bo2bo$
6b2o2$3b2o4b2o$2bo2bo2bo2bo$3b2o4b2o$4bo4bo12$b3o6b3o$o2bo6bo2bo$3bo6b
o$3bo6bo$2bo8bo!

[glider_rider]

Here's a way to do it with just a glider that I posted earlier.

Code: Select all

x = 15, y = 27, rule = B3/S23
3b2o2b2o$3b2o2b2o$2b3o2b3o$2b3o2b3o2$2bo6bo$2bo2b2o2bo$3b6o3$5b2o$4bo
2bo$4b4o$3b2o2b2o$o2bo4bo2bo$3bo4bo$4b4o$o10bo$bo8bo2$5b2o4$13bo$12b2o
$12bobo!

[towerator]

Here's a way to do it with just a glider that I posted earlier.

Code: Select all

x = 15, y = 27, rule = B3/S23
3b2o2b2o$3b2o2b2o$2b3o2b3o$2b3o2b3o2$2bo6bo$2bo2b2o2bo$3b6o3$5b2o$4bo
2bo$4b4o$3b2o2b2o$o2bo4bo2bo$3bo4bo$4b4o$o10bo$bo8bo2$5b2o4$13bo$12b2o
$12bobo!

Nice. I remembered it, but I coudn't re-find it, so I created something new instead.

[muzik]

Boat with tail:

Code: Select all

x = 15, y = 21, rule = B3/S23
7b2o$7b2o3$6bo2bo$3b2obo2bob2o$5b2o2b2o2$6b4o$5b6o2$6b4o$7b2o2$2o$2o2$
11b2o$11bobo$13bo$13b2o!

We've made some c/10 rakes... maybe we could look into making a copperhead-firing rake now?

[Dean Hickerson]

There's a fairly small p36 gun, so maybe I'll build yet another sawtooth using that. The design will have to be more complicated; with such a small period there's no room for the trigger between the pullers. But I'm sure it can be done, yielding an e.f. of 25/16.

This turned out to be more difficult than I expected, but I've finally dealt with all the problems that arose. So here's a sawtooth with expansion factor 25/16 = 1.5625, which I think is the smallest known, except for the parabolic sawtooth's e.f. of 1.

Code: Select all

#C Sawtooth with expansion factor 25/16
#C A collection of guns and other objects produces LWSS's heading
#C east toward a copperhead c/10 spaceships.  The LWSS's are of
#C 2 types, pullers and triggers.  The western part of the pattern
#C produces a p36 stream of salvos of 2 pullers.  (But p72 guns are
#C used to produce them.)  The eastern part produces triggers only
#C when needed.  When a trigger hits the copperhead, it turns into
#C a blinker, which is then pulled back to the west by the pullers.
#C When it's all the way back, a new trigger is released and the
#C blinker is deleted, allowing another group of pullers to follow
#C the new trigger.
#C
#C Deletion of the blinker is aided by two p36 guns and a p6
#C oscillator, located at the east end of the salvo producer.
#C
#C The production of a trigger is governed by a p576 gun in the
#C north middle part of the pattern.  The gliders from this gun are
#C usually deleted by tail sparks from the pullers.  But when the
#C blinker is pulled back far enough, one or two gliders cross the
#C pullers's path and a collection of signal duplicators and
#C reflectors create the trigger.
#C
#C Define a(0)=0 and a(n)=(25*a(n-1) - 9*(a(n-1) mod 16))/16 + 65
#C for  n >= 1.  Then, for  n >= 0,  a new group of pullers heads
#C east in gen  p(n) = 36*a(n).  A trigger is created in gen
#C t(n) = 36*a(n) + 947 - 16*(a(n) mod 16).  The trigger reaches
#C the copperhead in gen  b(n) = 45*a(n) + 974 - 4*(a(n) mod 16).
#C
#C n        0    1    2     3     4     5     6      7      8      9
#C a(n)     0   65  166   321   566   946  1542   2471   3922   6192
#C p(n)     0 2340 5976 11556 20376 34056 55512  88956 141192 222912
#C t(n)   947 3271 6827 12487 21227 34971 56363  89791 142107 223859
#C b(n)   974 3895 8420 15415 26420 43536 70340 112141 177456 279614
#C
#C The population is minimal some time around generations p(n), and
#C depends on  a(n) mod 80.  I haven't checked all 80 cases, so I
#C don't know the exact minimum repeating population; it's
#C somewhere around 5970.  (Even if we knew the minimum for each
#C case, we probably couldn't prove that all 80 occur infinitely
#C often.)
#C
#C The population is maximal around generations b(n), and is
#C approximately  7*b(n)/60.
#C
#C Dean Hickerson, 4/16/2016
#C
#C Credits:
#C
#C The c/10 spaceship, 'copperhead', was found by 'zdr', 3/5/2016:
#C http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2057
#C
#C The glider guns, with periods 36, 72, 144, and 576, are from
#C Jason Summers's updated version of Dieter Leithner and Peter Rott
#C gun collection:  http://entropymine.com/jason/life/dpguns/
#C
#C The period 8 glider reflector was found by Noam Elkies in 1998.
#C
#C The use of a block and a gun to duplicate a signal was
#C found by Dieter Leithner in 1993.
#C
#C The p6 oscillator is from the jslife collection at
#C http://entropymine.com/jason/life/p/jslife-20121230.zip
#C I don't know who found it.
x = 853, y = 248, rule = B3/S23
765b2o24b2o$765b2o24b2o$796b2o24b2o$796b2o24b2o$770b4o39b3o$770b6o36bo
3bo$773bobo34bo3b2o$774bobo6bo26bob2o$782b3o$772b2ob2o4b2ob2o$760b3o
10b3o31bo4bo20bobo2b2o$759bo2bo11bo6bobo23bo4bo19bo2bo$759bo2b2o18bobo
22bo4bo17b4obobo$759b2o2b2o17b6o41bob2o2bo$499bo21bo238b5o19b4o41b2o5b
2o$519b3o227b2o11bo43b2obo27bo$466b2o15b2o12b3obo16bo230b2o53b2o3bo24b
obo$330bo135b2o15b2o2bo8bob2o18b2o271b2o10bo3bo16b2o8bob2o$330b3o154b
3o6b2obo8b3o280b2o11b3o9bo7b2o9bo$333bo156bo3bob3o264bobo30b2o16b2o$
332b2o145bo9b2o17bobo5bo229b2o18bo9bo19b2o17b2o$473bo4b3o15bo12bo5bobo
224b2obo2bob2o10bo4bo2b2o5b2o44bobo$471bo2bo2bo2b2o10bo39b2o208bo4bo2b
2o10b2obo2bob2o4b2o44bo18b2o$470bo2bo2b2obo2bo8bobo21b3o14bo213bo19b2o
49b2o2bo4bo10b2obo2bob2o$470bo2bo3bob3o5b2o2b2o13b2o22bobo210bobo71b2o
bo2bob2o10b2o2bo4bo$237bob2o229bobo5b4o5b2o18bo22b2o289b2o19bo$232bo3b
o234bo32b3o13b2o321bobo$206bo10bo13b2o7bo103b2o144bo13bo15b2o$204b3o
10b3o12bo2b2ob2o94b3o6bo2bo143b2o$203bo5bo4bo5bo7b2ob2o2bo98bo2bo4bobo
bo142bobo$77b2obo80b2obo37bob6o4b6obo5bo7b2o96bo3bo2b3o2bo$81bo3bo79bo
3bo32bobo14bobo9bo3bo97bobob2o170b2o$77bo7b2o13bo10bo49bo7b2o13bo10bo
5b2o2bo2b2o4b2o2bo2b2o4b2obo103b2ob2o3b2o165b2o8b2o$78b2ob2o2bo12b3o
10b3o48b2ob2o2bo12b3o10b3o5b2o2bobo4bobo2b2o114b3o5bo135bo38bobo$12bo
69bo2b2ob2o7bo5bo4bo5bo51bo2b2ob2o7bo5bo4bo5bo4bobo12bobo6bo8bo232b4o
5bobo39bo4b2o$11b5obobo61b2o7bo5bob6o4b6obo49b2o7bo5bob6o4b6obo4bo14bo
5bo5b4o3bo230b3obo3bo2bo44bobo$11b2ob2obob3o12bo10bo36bo3bo9bobo14bobo
50bo3bo9bobo14bobo29bo4bo3bo229bo2bob2o2bo2bo46bo$13bobo16b3o10b3o39bo
b2o4b2o2bo2b2o4b2o2bo2b2o54bob2o4b2o2b2ob2o4b2ob2o2b2o24bo3bo8bo230b2o
2bo2bo2bo7b2o38b2o$20bobo8bo5bo4bo5bo48b2o2bobo4bobo2b2o66bob2ob2o4b2o
b2obo27b3o6bo234b3o4bo9bo2bo$14b3obob2ob2o5bob6o4b6obo31bo15bobo12bobo
54bo4bo6bob2o10b2obo19b2o16b2o94bo5b3o130bo$16bobob5o5bobo14bobo29bo3b
4o3bo7bo14bo50b3o3bo3bo7bo14bo20b2o112b2o3b2ob2o145bo2bo$23bo5b2o2bo2b
2o4b2o2bo2b2o28bo3bo6bo72b5obo3bobo34bo126b2obobo8b2o133bo2bo$31bob2o
2bo4bo2b2obo30bo8bo2b2o72bo8bo32b5o118bo2b3o2bo3bo7bo2bo23b2o87b2o18bo
bo29b2o$18b2o11bobo12bobo33bo5bo3b2o70b2o8bo31b3o3bo116bobobo4bo2bo8bo
bo24bo88b2o19bo30bo$14bob4o12bo14bo32b2o5bo3b2obo3b2o12b2o50b2o16b2o
20bo5b2o9bobo105bo2bo6b3o9bo3b2o18bobo138bobo$12b3o2bobo67bo6bo3b2o12b
2o68b2o23b4o10b2o107b2o20b2obo7b2o3b2o5b2o110b2o27b2o$24bo62bo2b4o99bo
11bo2b2o12bo130bo7bo6bobo102b2ob2o9b2o$14b2o8bo62bo2bob2o8bo88bo14b2o
145bo6bo2bo6bo102bo2bo23b2o$15bo7bobo10b3o7b2o39b2o11b2obo10b2o61bobo
11b3obo163b2o7b3o102b6ob2o18b2o$24bo11bobo7b2o45b2o6bobo74b2o11bo2b2o
29b3o131b3o113bo5bo$24bo11bob2o48b2obo2bo7bo75bo17bo27bo3bo128b3o116bo
4bo288b2o5b2o$41bo46b4o2bo98bobo32bo3b2o114b3o7b2o115bo4bo290bo5b2o$
35bo6bo44bo6bo99bo25b2o2bo3bobo2bo105bobo6bo6bo2bo6bo111bo17bo15b2o
258bobo$34bo7bo44bob2o3bo125b2o4b2o111b2o7bobo6bo7bo111b3o15b3o13b2o
259b2o$33b2o2b2ob2o46b2o3bo81bo164bo8b2o3b2o7bob2o121b2ob2o5bo22b2o
253b2o$25bo7b3o2bo50b2o2bo6bobo72bo45bo8b2obo128b2o3bo119bobobo5b2o22b
obo251bobo$25bo7b2o49b2o5bo9b2o65b2o4bobo43bobo9bobo2b2o127bobo120bobo
15b2o14bo252bo$24bobo7bo49bo2bo3bo4b2o3bo66b2o5bo4b2o33b2o2bo2bo10bo4b
o126bo2bo122bob2o14bo13b2o247bo$25bo9bo60b2o77bo3bo2bo32b2obo15bo106b
2o11bo11b2o113b2o2bo2bo2bobo6bo5b3o$25bo143bo9bo39b2o13bo2bo103bo2b6o
3bobo125b2o3bobob2obo5b3o5bo262b3obo$18b2o64bob2o8bo71bobo8bo162b2o6b
4obo131b2o3bo5bo270bob2o$18b2o10b2o47b2o2bobo9bobo65b2o2bo2bo8bobo3bo
144bobo6b3o13bob2o130b3o7b2o268b2obo$30b2o47bo4bo10bo2bo2b2o60b2obo13b
obo3bo16bobo110b2o12b2o7bo2bobo5b2o2b2ob2o130bo19b2o256bob3o$30b2o8bo
42bo15bob2o64b2o12bo4bo16b2o112bo13bo8b2o13bo153bo$18b3o9bo10bo38bo2bo
13b2o83b4o18bo112bobo27b2o4bobo154b3o256bo$13b2o2bob2o8bobo7b3o276b2o
27b2o4b2o157bo$13b2o2b2o11bobob3o158bobo$17b2o12bob4o159b2o$32bo33bo2b
o32bo2bo32bo2bo32bo2bo18bo13bo2bo14bo2bo14bo2bo14bo2bo14bo2bo14bo2bo
14bo2bo$70bo35bo35bo35bo35bo17bo17bo17bo17bo17bo17bo$7bo58bo3bo31bo3bo
31bo3bo31bo3bo31bo3bo13bo3bo13bo3bo13bo3bo13bo3bo13bo3bo13bo3bo$5b3o
59b4o32b4o32b4o32b4o32b4o14b4o14b4o14b4o14b4o14b4o14b4o$4bo3b2o$3bob2o
3bo3bobo101bobo79b2o$3bobo3b2o3bob2o17b2o82b2o78bobo$2b2obo2b3o7b2o16b
2o14bo2bo30bo32bo81bo$5bobobo6bo2b2o14bo19bo28b3o63b2o34b2o34b2o16b2o
16b2o16b2o16b2o16b2o409b2ob2o$5bobobo6b2o2bo30bo4bo13b4o9bo3b2o59b2ob
2o31b2ob2o31b2ob2o13b2ob2o13b2ob2o13b2ob2o13b2ob2o13b2ob2o407bo3b4o$4b
2ob2o9b2o26b2o3b2o2bobo11bo4bo7bob2obobo5b2o51b4o32b4o32b4o14b4o14b4o
14b4o14b4o14b4o408bo3b4o$45b2o9bob2o8bobo3bo7bobo2bo2bo4b3o16b3o32b2o
34b2o34b2o16b2o16b2o16b2o16b2o16b2o405b2o2b2o$47bo19bobo3bo7b2obo9b2ob
3o16bo601b2o2b2o$67bo16bobo8bo3bo15bo606bo3b4o$56bo2bo7bo16bobobo6b2o
2bo81b2o49b2o51b2o4b2o33bo395bo3b4o$4b2ob2o47b2o9bo2bo12b2ob2o8b3o21b
3o57b4o48b2o50bobo4b2o16b2o14bobo395b2ob2o$5bobobo22b2o34b2o50bo11b2o
31bo13bo2bobo99bo13b2o10b2o9bobo2b2o$5bobobo22bo2bo26bo58bo9b4o26b4obo
11bobo2b2o96b2obo12bo2bo8bo11b2o2bo2b2o$2b2obo2b3o50b3o66bobo2bo13bo
11b3obobo9bobo101b2obobob8o2b3o25bobo$3bobo3b2o3b2o37b2o5b2ob2o65b2o2b
obo11bob4o12bobo7b2o106bobo9b2o23b6obo347b2o24b2o111b2o$3bob2o3bo3b2o
16bob2o12b2ob3o7b3o19b2ob2o47bobo9bobob3o13bo8b3o59b2o44bobo11bo22bo5b
o296b2o24b2o24b2o24b2o58bo52bo8b2o15b2o$4bo3b2o17b2o2bobo13bo14bo21bob
obo22b2o24b2o7bobo17b2o9bobo57b2o33b2o11bo3bo5bob2o25b3o297b2o23bo2bo
40b3o65bobo49bobo8b2o15b2o$5b3o19bo4bo17bob2o30bobo24b2o23b3o8bo18b2o
10b2o59bo31bo2bo17b2o30bo307b2o16bobo39bo3bo63bo3bo48b2o15bo$7bo23bo
13bobobo2b3o26b2obo50bobo9b2o17b2o4b3o7b2o87bobo357bo2bo16bo38bo3b2o
65bo3bo60b4obo$17b2o9bo2bo13b2o35bobo2bo2bo2b2o40b2o4b2o4b2o32bobo88bo
3b2o22b2o330b2o14b2o40bob2o68bo3bo59b4o2bo$17b2obo2b3o56bob2obobo3b2o
16b3o26bo2bo3b2o27bo6bo37b3o49b2obo7bo2b2o3bo8b2o344bo2bo112bo3bo40bo
21bobo$11bo6b8o37bo19bo3b2o17b2o2bob2o29bo25b3o2b3o46bo50bo7bo2bob3obo
b2o5bo346bo2bo113bobo41b2o23bo$10bo8b4obob2o12b2o8b3o9b3o19b3o19b2o2b
2o27b2o28b2ob2obo46bo51bo7bobo2b3o4bo341b2o9bo2bo9b2o2bobo20bo4bo72bo
41bobo20bo2bo5bo$5bobo2b2obob4o8bo12b2o7bo2bo8b2ob2o6bo13bo23b2o28bobo
2bo25b2o2b2o40bo65bo6bo3bo342b3o8b2o14bo2bo19bo4bo76bo60bo2bo4bobo$4bo
2bo4b7o7bo24bo10b3o7b2o22b3o4bo37bo4bo27b2o17bo23b2o50bo21b3o368bobob
4o17bo4bo75bobo45bo13b2ob2o3bobo$4bo7b3o2bobo43bo35bo4bo35bo43b2o6bob
2o20bobo48b3o21bo319b2o12b2o9b3o25bo2b2obo98b2o44b2o14bo2bo4bo$7bo60bo
bo2b3o20bo25b2o16bo5bo37bobo8b2o69bo3bo6bo332bo2bo14bo9b2o22b2o5b2o94b
2o48bobo$2bobobo20b4o9b3o10b3o12b4obo15bobo3bo7bob2o15bobo15bo2bobo24b
2o11bo6bo2b3o70bo4b3o2bobo7bo11b3o312bo11bobo34bo23b2obo74bobo$b4o4b3o
14bo4bo7bob4o6b4obo11b2o15bo3b2obo6b2o3bobo14bo2bo13b3o2bo25b2o2b2o9b
2o5b2o73b2obob3obo2bo7bo10bo2bo284bo24b3o13bo36bobo18b2o3bo74bo5b2o$9b
2o15bo3bobo6bo2bo2bo4bo2bo2bo26b3o12bo23b2o13bo5bo26bob2ob2o3b2o81b2o
3bo3b2o2bo7bob2o9b2obo7b2o276bo55b2o18b2obo8b2o7bo3bo75b2o5b2o$10b2o
15bo3bobo3b2o4b3o4b3o4b2o32bo4bo23b3o20bo18b2o5b3o2b3o3b2o11b3o66bobo
18b2o3bo18bo2bo273b3o21b2o12b2o17bo2bo19bo9b2o8b3o$3b4o3bo22bo4bobo14b
obo5b3obo2bobo9bobo7bo14b2o10b2o12b2o2bo4bo21bo4bo92bo24bobo16bobobo
297b2o12b2o18b2o58b2o$bobobo7b2o18bo4bob6o4b6obo6bobobobo2bo6b2ob2o4bo
16b4o9b2o12b2o3bo2bobo7b2o8bo99b2o23bo2bo14b3o2bo340b2o50b2o123bo4bo2b
o$o9b2obo16bo2bo5bo5bo4bo5bo16bo6b2ob2o3bobo14bobo2bo32b2o5bo10bo3bo5b
3o82b2o29b2o8bo352b2o22bobo149bobo3b2ob2o$3bo7bo19b2o7b3o10b3o10bo14b
2o22b2o2bobo28bo12bo7bo3b4o11b2o12b2o59b2o40bobo6b2o349b2o18bo148bobo
4bo2bo$o2bo7bo30bo10bo12bo2bobobobo7b2o5bo19bobo27bo2bo5bo3bo9bo15bo2b
2o8b2o2bo60bo49bo297b2o18bo27b2obo2bob2o10bo4bo2b2o144bo5bo2bo$obo64bo
bo2bob3o4b2ob2o3b2o21b2o5b2o12b2o6b2o3b4o3bo25bo4b2o4b2o4bo101bo2bo
299b2o4b4o10b2o2b2ob3o22bo4bo2b2o10b2obo2bob2o137b2o11bo$81b2ob2o3b5o
17b3o4bo2b2o8b2o2bo15bo25b2o3bob2o4b2obo3b2o100b3o299b2o2b2ob3o10b2o4b
4o26bo19b2o139bo2bo12bobo$81bobo5b2ob2o16bobo5bo4b2o4b2o4bo27b2o6b2o5b
obo14bobo5b3o94b4o301bo19b2o27bobo177bo2b4o$90bo19b2o4b2o3bob2o4b2obo
3b2o5bo19b3ob3obo6bob6o4b6obo7bo30b3o63b3o513bo2bo13bob4o$80b3o34bobo
14bobo5b5obobo11bo2bob2o2bo7bo5bo4bo5bo7bo30bo2bo63bo2bo513bo2bo13bo$
80bo36bob6o4b6obo5b2ob2obob3o7bo2b2obo2bo10b3o10b3o3bo38bo57bo523bobo
18b2o$118bo5bo4bo5bo8bobo13bob3ob3o13bo10bo5b2o37bo57b2o6bobo477b2o35b
o19b2o$119b3o10b3o16bobo5b2o6b2o29bobo34bobo68bo477b2o48bo$121bo10bo
12b3obob2ob2o138bo2b3o520b2o12bo$147bobob5o137bobobo522b2o5bob2obo$
154bo138bo2bo530b2obo$63b2o64b2o6b2o155b2o7bob2o519bo4b4o$62b3o39bo10b
o13b3ob3obo165bo2bo387b2o5bo125b2o$63bobo6b3o18b2o7b3o10b3o10bo2bob2o
2bo165b3o388b2o6b2o128bobo$63b2o2bo8bo16b2o6bo5bo4bo5bo7bo2b2obo2bo
565b2o128b3o$63b3obo3bo4bo16b2o5bob6o4b6obo6bob3ob3o139b2o555b2o$67b2o
6bo18bo5bobo14bobo5b2o6b2o138b2o555bobo$63b2o7b2o19bobo3b2o3bob2o4b2ob
o3b2o154bo554b2o$67b2o3bo15b3obobo6bo4b2o4b2o4bo187b2o$63b2o7bo15b4obo
7bo2b2o8b2o2bo15bo171bo$64bob3o3bo19bo9b2o12b2o11b4o3bo48b3o119b3o495b
2o13b2o$64bo2b2o55b3o5bo3bo50bo121bo495bobo12bo2bo2b2o$66bobo67bo49bo
618bo20b2o$67b3o5bo52bo4bo47bo638bo2bo$67b2o7b2o8bo15b2o11b3o3b3o2b3o
5b2o45b2o111b2o13bo2bo460b2o44bo2bo$75bo8b2o16b2o17b2ob2obo52bobo93bo
13b2obo15bo462bobo44bobo$86bo19b2o5b2o8b2o2b2o146b2o13b2o2bo2bo10bo4bo
460bo45bo$105bo6bo2b3o8b2o117b2o18b3o8bo18bobo9bobo2b2o$91b2o13bobo8b
2o124bo2bo16bo8b2obo20bo8b2obo511b2o$69bo13bo6b4o12b2o6bob2o145bo4bo2b
o4bo543b2o$67b3o11bobo5bobo2bo20bo6b2o140bo10bo19b2o552b2o$66bo3b2o10b
2o5b2o2bobo25b2o2b2o116b2obo19b2o3b2o22b2o4bo3bo2bo518b2o20b3o$65bob2o
3bo3b2o16bobo25bob2ob2o116bobo2b2o15bo7b2o24bo5b2o514b2o2b2o2b2o10b2o
2bo2bobo$65bobo4bo3b2o18b2o23b3o2b3o117bo4bo15bo4bo19b2o7bo521b2o2bo2b
obo10b2o2b2o2b2o$64b2obobobo23b3o23bo33b2o90bo19bo3bo4bo14b2o324bo20bo
24b2o164b3o15b2o$67bo3bo22bobo46b2o10bo91bo2bo21bob2o17bo3b3o3b3o310b
2o18b3o24b2o2b2o160b2o$67bob2o23b2o27b3o4b2o10bo2bo11bo113bo343bob2o
16bo31bobo132b2o$66b2ob2o47b2o10b2o9bo2bobo6b5o99bo7b2o4b2o28b2o311b3o
2bo15b2o31bo2b2o129b2o$80bo37bobo9b2o9b3o2bo2bo3bo6bo6b3o80bobo4bo7b3o
3bo9bo18b3o313bobobo199b2o8b2o$79b4o36b3o8bo15bobobo5b5o8bo66b3o11b3o
7bo4bobo12b2o4b4o11bo315bobobo43b2o2bo3bo142bo2bo2bo7b2o7b2o$78bo3bo
37b2o7bobo7b3ob2obobo2bo4bo11bo66bo2bo12b2o7bo18bo3bo6bo11bo315bo2b3o
15b2o25bo2bo4bo141bo3b2o16bob2o$77bo3b2o35bobo9bobob3obo2b2o3b2o4bo3bo
bo4bo74bo40b2ob2o4b3o10b3o315b2obo16b2o22b3o5bobobo139b3o18b3obo$66b2o
b2o7b3o32b2o2bobo11bob4ob2o3bo2bo7bo2b2o4b2o73bo41bob2o17b2o317b2o41bo
8bobobo159b2ob2o$67bob2o7bo5bo20bo7bobo2bo13bo11b2obo6bo7bobo70bobo7b
2o23bo9bo12b2o325bo3bo48bo4bo134b3ob3o19b2o3bo$67bo3bo7bobob2o20bobo6b
4o30b6o93bob2o19b3o7bo12b2o3b3o3b3o4b2o310bobo48bo3bo134b3ob2o18bobo2b
2o$64b2obobobo10bobo20b2o8b2o126bo2bo2b2o17b2o3bo7b2o27bo313b2o187b2o
2b2o19bo2bo$65bobo4bo7b2o161bobo13bobo5bobob2obo6bo20bo10bo306b2o53b2o
136b2ob3o22b3o$65bob2o3bo28bo142bo23bobobobo27bo6bo3bo305bobo190b3ob3o
23bo$66bo3b2o27bobo155bobo2bo9bob2o3bo14bo7bo3b4o3bo305bo5b2o110bo$67b
3o30b2o34b2o106b2o10b2obo9bo2bo5bobo12bobo15bo306b2o5b2o111b2o74b3o$
69bo64b2ob2o105b2o3bobo5bo3bo8bobo5b2o2bobo4bobo2b2o441b2o71b2o3bo$
134b4o30b2o38bo40b2o7b4o7b2ob2o2b2o2bo2b2o4b2o2bo2b2o511bo2bo2bo$76bo
2bo13b2o9b2o29b2o30bobo36b3o41bo8bo17bobo14bobo5b3obo2bobo498b2o$79bo
15bob2o6b2o58b3o37bo3b2o66bob6o4b6obo6bobobobo2bo489b2o24b2o$75bo4bo
10bo2bo2b2o5bo56b2obo3bo35bob2o3bo3b2o61bo5bo4bo5bo16bo489b2o24b2o$75b
2o2bobo9bobo65bo5bob2o35bobo4bo3b2o62b3o10b3o10bo$80bob2o8bo56b3o7bo5b
o37b2obobobo58b2ob2o7bo10bo12bo2bobobobo$151bo7bo5bob2o37bo3bo59bobo
33bobo2bob3o423b2o$92b2o56bo10b2obo3bo37bob2o59bo2bo466b2o2b2o$80bo2bo
3bo4b2o71b3o37b2ob2o62bob2o319b2o19bo126bobo$80b2o5bo79bobo92b2o4bobob
obo316b4o4b2o10b3ob2o2b2o123bo3bo$87bo80b2o92b2o3bobob2obo316b3ob2o2b
2o10b4o4b2o3b3o120b2o$193bo74b2o3bo322bo18b2o9bo114b2o3bob2o$83b3o3b3o
91bo8b2o76b3o352bo116bo2b3o2bo$162b2o19bo9bo11b2ob2o9b2o6b2o41bo369b2o
97b3o5bobobo$86b2o73bo2bo16bob2o4b2obo13bob2o8bo2bo4bobo4b2o405b2o97bo
8bobobo$86b3o7bo64bo18b2o6bo4bo12bo3bo6b2ob2o6bo4bobo362b2o12b2o135bo
2b3o$87bo7b2o4b4o56bo22bo7bo10b2obobobo6bobo14b3o18b2o13bo2bo324b2o12b
2o136b2obo$86bo7bo3bo6bo47b3o5bobo3bo15b2o3b2o14bobo4bo3b3o17b2o9bo4b
2obo15bo364b3o113b2o$85b3o6b2ob2o4b3o46bo2bo6bobo3bo15b2o6b2o10bob2o3b
o3b2o16bobo9b2o4b2o2bo2bo10bo4bo334b3o21bo117bo$86b2o7bob2o56bo7bo4bo
14b3o3bo15bo3b2o17b2o2bobo10bobo8bobo9bobo2b2o333bo22b3o$95bo12b2o45bo
8b4o20bo4bo12b3o19bobo2bo23bo8b2obo338bo2bo19bo$76b2o4b3o3b3o4bo12b2o
42bobo34bob2o15bo7bobo10b4o376b2o12b2o5bo3bo$78bo17b2o82bo7bo26bo3bo
10b2o24b2o364bo2bo4bo2bo$75bo10bo9bo34b3o37bo7b3o6b2o35bo30b2o8bo2bo
351bo3bo5b2o$75bo3bo6bo46bo36b3o5b2ob2o5bo23b2o5b4ob2obo34bo5b2o354bo$
75bo3b4o3bo7bo14bo22bo36b2ob2o5b3o29bo3bo7bo4bo32b3o358b3o$77bo15bobo
12bobo59b3o7bo25b2o3bo4bo7bo3bo31bobobo357bo$93b2o2bobo4bobo2b2o60bo
34b3o3bob2ob4o5b2o24bobo4b3ob3o352b3o$91b2o2bo2b2o4b2o2bo2b2o50bo2bo
38bobo6bo33bo3bobo5bobobo$77bobo2bob3o5bobo14bobo51bo23bo15bo2b2o12bo
3bo23bobo3bo6b3o$76bo2bobobobo6bob6o4b6obo50bo4bo19b3o13bob3o3bo9bobo
7bo15b2o3bo9bo351b2o24b2o$76bo16bo5bo4bo5bo50bobo2b2o17b2o3bo11b2o7bo
15b4obo12bobo3bo2bo359b2o24b2o$83bo10b3o10b3o49b2obo21bo3b2obo14b2o3bo
15b3obobo11b2o5b2o$74bobobobo2bo12bo10bo63bo3bo8b2o3bobo10b2o7b2o19bob
o28bo$73b3obo2bobo88b2ob2o8b3o2bob2o13b2o6bo18bo16b3o9b3o$159bo2bo9bob
2o3b2o4bobobo12b3obo3bo4bo16b2o6b2o8bobo8bobobo$161b2o9bo6bobo3bobobo
12b2o2bo8bo16b2o6b2o10bo7b3ob3o5b2o$125bo48bo4bo6b2ob2o11bobo6b3o18b2o
27bobobo5bo$123b3o46bo2bo4bo20b3o58b3o9bo$122bo3b2o44bo29b2o59bo6bo3bo
$121bob2o3bo3b2o28bobo8bobo64bo14bo11b4o3bo$113b3o5bobob3o4b2o28b2o12b
o62bobo12bobo15bo$115bo4b2obo2bo36bo11b2o9b2ob2o48b2o2bobo4bobo2b2o$
114bo8bo61bobobo47b2o2bo2b2o4b2o2bo2b2o4b2obo$123bobo59bobobo48bobo14b
obo9bo3bo$122b2ob2o9b2o46b3o2bob2o45bob6o4b6obo5bo7b2o$135bo2bo9b2o29b
2o3b2o3bobo47bo5bo4bo5bo7b2ob2o2bo$97bo40bo8bobo29b2o3bo3b2obo48b3o10b
3o12bo2b2ob2o$82b2o12bob4o32bo14bo35b2o3bo51bo10bo13b2o7bo$78b2o2b2o
11bobob3o30b3o3b2o47b3o78bo3bo430b2o5b2o$78b2o2bob2o8bobo25b2ob2o5bo5b
o20bo27bo85bob2o426b2o5bo$83b3o9bo27bobo6b3o15b2o6b2o548bobo$95b2o26bo
12bo2bo2bo7b2o6bobo8bo2bo535b2o$95b2o23b2obo2bo10b5o8b2o20bo531b2o$83b
2o10b2o24bobob3o10b3o10bo16bo4bo13b4o513bobo$83b2o36bob2o3bo21bobo15b
2o2bobo11bo4bo513bo$90bo31bo3b2o17b3obobo21bob2o8bobo3bo517bo$90bo18bo
13b3o19b4obo33bobo3bo517b3o$89bobo18bo14bo23bo34bo522b3obo$90bo4b3o12b
2o61bo2bo7bo523bo3bo$90bo6bo8bo2b3o61b2o4b2o3bo2bo521bo3bo$96bo6b2ob2o
2b2o29bo37bobo3b2o523bob3o$102bo7bo21bo6b2ob2o33b2o519b2o11b3o$102bo6b
o13b2o5b2ob2o6bo35b3o514b2o2b2o12bo$103bo19b3o6bo44b2o514bobo$89bo15b
2obo13bobo53b2o514bo$89bo7b2o7bobo11bo2b2o53b2o$80bo7bobo6b2o7b3o11bob
3o23b2o10b2o15b3o510b2o4b2o$79b2o8bo29b2o6b3o14b2o2b2o9b2obo15b2o2bo
505bob2o4bo$89bo33b2o2b2o15b2o2bob2o7bo2bo13b3ob2o505bo9b3o$77b3o2bobo
34b2o7b2o19b3o6bo2bo14b2o2b3o507bo8bo$79bob4o12bo14bo10b2o3bo28b2ob2o
18b2o504b2obo$83b2o11bobo12bobo5b3obo7b2o38b2o7b2o504b2o$96bob2o2bo4bo
2b2obo5b2o2bo4b2obo17b2o6b2o12b2o8b2o6bo$88bo5b2o2bo2b2o4b2o2bo2b2o3bo
bo7bo19b2o29b3o6b2o$81bobob5o5bobo14bobo3b3o8bo51b2o$79b3obob2ob2o5bob
6o4b6obo4b2o57bobo4bobo2b3o$85bobo8bo5bo4bo5bo43b3o10b3o6b2o4b4obo$78b
obo16b3o10b3o43bob4o6b4obo11b2o$76b2ob2obob3o12bo10bo45bo2bo2bo4bo2bo
2bo$76b5obobo69b2o4b3o4b3o4b2o4b2obo$77bo77bobo14bobo9bo3bo$155bob6o4b
6obo5bo7b2o$156bo5bo4bo5bo7b2ob2o2bo$157b3o10b3o12bo2b2ob2o$159bo10bo
13b2o7bo$185bo3bo$190bob2o!

I doubt that the expansion factor can be reduced much more using copperheads. Probably a p34 version could be built, giving e.f. 49/32 = 1.53125, but p34 and p68 guns are so large that I don't want to build it. There might be a salvo of spaceships that can pull something faster than the blinker is pulled here, but I haven't found one.

A slower orthogonal spaceship (with an appropriate tail spark) could lead to a smaller e.f. In general, if a sawtooth is built using spaceships of speed alpha*c that catch up with a spaceship of speed beta*c, and salvos are produced every P gens which pull some object N units, then the e.f. is 1 + alpha*beta*P / ((alpha-beta)*N). So we could get arbitrarily close to 1 if beta is close to 0.

[Dean Hickerson]

I doubt that the expansion factor can be reduced much more using copperheads.

I was wrong. Today I thought of a simpler way to build a sawtooth, with expansion factor 3/2. Instead of having the LWSS's pull something, one of them releases a MWSS from a stifled rake, which then deletes the subsequent LWSS's. So now the gun part of the pattern is much simpler; it's just a p256 LWSS gun and an eater. Most of the complexity is now at the moving end of the pattern, and that's just 4 rakes.

If I'd thought of this earlier, I could have saved myself a lot of time and frustration!

Code: Select all

#C Sawtooth with expansion factor 3/2
#C A group of 4 eastward c/10 rakes produces and destroys a westward
#C MWSS every 320 gens.  Meanwhile a gun makes an eastward LWSS every
#C 256 gens.  When the first LWSS reaches the rakes, it deletes one
#C glider, allowing a MWSS to escape.  The MWSS deletes subsequent
#C LWSS's.  Eventually it reaches the gun, where it's deleted,
#C allowing more LWSS's to escape.
#C
#C Let  a(0) = 0  and  a(n) = floor(3*a(n-1)/2) + 2  for  n >= 1.
#C Then, for  n >= 0,  a LWSS deletes a glider, releasing a MWSS,
#C in gen  r(n) = 320*a(n) + 449;  the MWSS is deleted in gen
#C d(n) = 384*a(n) + 645.
#C
#C    n    0    1    2    3    4    5     6     7     8     9    10
#C a(n)    0    2    5    9   15   24    38    59    90   137   207
#C r(n)  449 1089 2049 3329 5249 8129 12609 19329 29249 44289 66689
#C d(n)  645 1413 2565 4101 6405 9861 15237 23301 35205 53253 80133
#C 
#C The population is maximal at some time near r(n), and is
#C approximately  3*r(n)/320.
#C
#C The population is minimal at some time near d(n), and depends
#C on  a(n) mod 10:
#C
#C a(n) mod 10        0     1    2    3    4    5    6    7    8    9
#C min population  3226  3236 3222 3222 3234 3231 3222 3226 3227 3231
#C
#C I conjecture that a(n) takes every value mod 10 infinitely often,
#C in which case the minimum repeating population is 3222.
#C
#C Dean Hickerson, 4/17/2016
#C
#C Credits:
#C The p256 gun was found by Dave Buckingham in September 1995.
#C The p320 c/10 rakes were found by Nico Brown and towerator in
#C March 2016.
x = 347, y = 347, rule = B3/S23
128b4o7bo$128bo3bo6bo107bo7bob2o$127bo12bo2bo102b3o5bo6bo$127bo3b2o5b
3ob2obo99bo4bo2b2o3bo2bo$127bo6b2o6b2ob2o97b3o4bobo5b2o$127bo6b2o6b2ob
2o97b3o4bobo5b2o$127bo3b2o5b3ob2obo99bo4bo2b2o3bo2bo$127bo12bo2bo102b
3o5bo6bo$108b2o18bo3bo6bo107bo7bob2o$107b2ob2o5b3o8b4o7bo9b2o83b2ob2o$
107bo2b2o10bo25b2ob2o5b3o64b3o5bo3b4o34b2ob2o$85b2o20b4o6b2o3b3o23bo2b
2o10bo60bo2b3o3bo3b4o25b3o5bo3b4o$84b2ob2o5b3o10b2o4b2o3b2o2bobo23b4o
6b2o3b3o45b2ob2o8bo3bobo2b2o30bo2b3o3bo3b4o$84bo2b2o10bo7b2o4b2o3b2o2b
obo23b2o4b2o3b2o2bobo36b3o5bo3b4o6bo3bobo2b2o30bo3bobo2b2o$84b4o6b2o3b
3o5b4o6b2o3b3o23b2o4b2o3b2o2bobo35bo2b3o3bo3b4o6bo2b3o3bo3b4o24bo3bobo
2b2o$84b2o4b2o3b2o2bobo5bo2b2o10bo25b4o6b2o3b3o35bo3bobo2b2o13b3o5bo3b
4o24bo2b3o3bo3b4o$84b2o4b2o3b2o2bobo5b2ob2o5b3o28bo2b2o10bo37bo3bobo2b
2o22b2ob2o27b3o5bo3b4o$84b4o6b2o3b3o6b2o38b2ob2o5b3o40bo2b3o3bo3b4o57b
2ob2o$84bo2b2o10bo49b2o51b3o5bo3b4o$64b2o18b2ob2o5b3o114b2ob2o$63b2ob
2o5b3o9b2o103b2ob2o$63bo2b2o10bo102b3o5bo3b4o$63b4o6b2o3b3o99bo2b3o3bo
3b4o70bo$63b2o4b2o3b2o2bobo99bo3bobo2b2o74b2ob2o$63b2o4b2o3b2o2bobo99b
o3bobo2b2o74bo$63b4o6b2o3b3o99bo2b3o3bo3b4o68bo3bo$63bo2b2o10bo78b2o
22b3o5bo3b4o69b3o$63b2ob2o5b3o80b2ob2o5b3o21b2ob2o88b2ob2o$64b2o90bo2b
2o10bo102b3o5bo3b4o$156b4o6b2o3b3o99bo2b3o3bo3b4o$156b2o4b2o3b2o2bobo
99bo3bobo2b2o$156b2o4b2o3b2o2bobo99bo3bobo2b2o$156b4o6b2o3b3o99bo2b3o
3bo3b4o$156bo2b2o10bo102b3o5bo3b4o$156b2ob2o5b3o114b2ob2o$157b2o5$80b
2o$79b2ob2o5b3o114b2ob2o$79bo2b2o10bo102b3o5bo3b4o$79b4o6b2o3b3o99bo2b
3o3bo3b4o$79b2o4b2o3b2o2bobo45b2o52bo3bobo2b2o$79b2o4b2o3b2o2bobo44bob
o52bo3bobo2b2o$79b4o6b2o3b3o46bo52bo2b3o3bo3b4o$79bo2b2o10bo102b3o5bo
3b4o$79b2ob2o5b3o114b2ob2o$80b2o12$119bo$117bobo$118b2o28$230b2o$231b
2o$230bo$254bo$255b2o$254b2o$42b2o$42b2o5b2o29b2o$49b2o28b2ob2o5b3o
114b2ob2o$79bo2b2o10bo102b3o5bo3b4o$79b4o6b2o3b3o99bo2b3o3bo3b4o$18b2o
8b2o17b2o30b2o4b2o3b2o2bobo99bo3bobo2b2o$18b2o9bo17b2o30b2o4b2o3b2o2bo
bo99bo3bobo2b2o$29bobo21b2o24b4o6b2o3b3o99bo2b3o3bo3b4o$30b2o21b2o24bo
2b2o10bo102b3o5bo3b4o$12b2o65b2ob2o5b3o114b2ob2o$12b2o66b2o$16b2o$16b
2o3$157b2o$11b2o143b2ob2o5b3o114b2ob2o$11b2o41bo101bo2b2o10bo102b3o5bo
3b4o$52b3o101b4o6b2o3b3o99bo2b3o3bo3b4o$51bo104b2o4b2o3b2o2bobo99bo3bo
bo2b2o$51b2o103b2o4b2o3b2o2bobo99bo3bobo2b2o$156b4o6b2o3b3o99bo2b3o3bo
3b4o$64b2o90bo2b2o10bo102b3o5bo3b4o$63b2ob2o5b3o80b2ob2o5b3o21b2ob2o
88b2ob2o$63bo2b2o10bo55b3o20b2o22b3o5bo3b4o$63b4o6b2o3b3o52b2o3bo41bo
2b3o3bo3b4o$63b2o4b2o3b2o2bobo51b2o2bobo41bo3bobo2b2o$63b2o4b2o3b2o2bo
bo52bo5bo40bo3bobo2b2o$18b2o43b4o6b2o3b3o53b2o2bo41bo2b3o3bo3b4o$19bo
43bo2b2o10bo59bo42b3o5bo3b4o$16b3o44b2ob2o5b3o9b2o103b2ob2o$16bo41b2o
4b2o18b2ob2o5b3o114b2ob2o$58b2o24bo2b2o10bo36b2o11b2o51b3o5bo3b4o$35bo
48b4o6b2o3b3o6b2o26bo11b2ob2o5b3o40bo2b3o3bo3b4o57b2ob2o$35b3o46b2o4b
2o3b2o2bobo5b2ob2o5b3o28bo2b2o10bo37bo3bobo2b2o22b2ob2o27b3o5bo3b4o$
35bobo46b2o4b2o3b2o2bobo5bo2b2o10bo25b4o6b2o3b3o35bo3bobo2b2o13b3o5bo
3b4o24bo2b3o3bo3b4o$37bo15b2o29b4o6b2o3b3o5b4o6b2o3b3o23b2o4b2o3b2o2bo
bo35bo2b3o3bo3b4o6bo2b3o3bo3b4o24bo3bobo2b2o$53b2o29bo2b2o10bo7b2o4b2o
3b2o2bobo23b2o4b2o3b2o2bobo36b3o5bo3b4o6bo3bobo2b2o30bo3bobo2b2o$57b2o
25b2ob2o5b3o10b2o4b2o3b2o2bobo23b4o6b2o3b3o45b2ob2o8bo3bobo2b2o30bo2b
3o3bo3b4o$57b2o26b2o20b4o6b2o3b3o23bo2b2o10bo60bo2b3o3bo3b4o25b3o5bo3b
4o$16b2o89bo2b2o10bo25b2ob2o5b3o64b3o5bo3b4o34b2ob2o$16b2o89b2ob2o5b3o
29b2o83b2ob2o$22b2o27b2o55b2o$22b2o27b2o203bo$254b2obo$254b2obo5b3ob2o
$20b2o233b2o3bo4b2o2b2o$20b2o5b2o230b2o5bo4bo$27b2o230b2o5bo4bo$255b2o
3bo4b2o2b2o$254b2obo5b3ob2o$254b2obo$256bo$72b2o$16b2o47b2o5b2o$9b2o5b
2o47b2o$9b2o$108b2o$67b2o17b2o8b2o9bobo$11b2o27b2o25b2o17bo9b2o9bo$11b
2o7bo19b2o19b2o21bobo19b2o$5b2o13b3o38b2o21b2o$5b2o11bo4bo78b2o$17b4o
3bo21b2o54b2o$16b2ob2o25b2o50b2o$17bo5bo18b2o54b2o$18b2o2bo19b2o$21bo
2$103b2o$47b2o54b2o$5bo41b2o$5b3o$8bo$7b2o7$96b2o$40b2o54bo$40bo56b3o$
41b3o12b2o41bo$2o41bo12b2o15bo$2o74b3o$74b2o2bo$72b4ob2o$61b2o11b3o$5b
2o54b2o$5b2o50b2o$b2o54b2o$b2o72b2o21b2o$19b2o21b2o30bobo21b2o$18bobo
21b2o19b2o9bo17b2o$7b2o9bo17b2o25b2o8b2o17b2o$7b2o8b2o17b2o2$94b2o$38b
2o47b2o5b2o216b2o$31b2o5b2o47b2o223bobo6b2o2bo$31b2o278bo2b2o5b2obo2bo
$312b2o3bo4bo4bo$312bo5bo4bo2bobo$312bo5bo4bo2bobo$312b2o3bo4bo4bo$
311bo2b2o5b2obo2bo$312bobo6b2o2bo$312b2o$169bo$168bobo5bo33bo71b3o$
167b2obo3bo2bo2bo28bobo5bo64b3o4b3ob2o28b3o$146bo22bo3bo3bobob2o25b2ob
o3bo2bo2bo58bo7b3o4bobo25b3o4b3ob2o$145bobo5bo18bo7b2ob2o25bo3bo3bobob
2o35b3o24b2obo4bo2bo23bo7b3o4bobo$144b2obo3bo2bo2bo14bo7b2ob2o28bo7b2o
b2o33b3o4b3ob2o14b2obo4bo2bo29b2obo4bo2bo$146bo3bo3bobob2o9bo3bo3bobob
2o30bo7b2ob2o31bo7b3o4bobo5bo7b3o4bobo29b2obo4bo2bo$149bo7b2ob2o5b2obo
3bo2bo2bo29bo3bo3bobob2o39b2obo4bo2bo7b3o4b3ob2o26bo7b3o4bobo$149bo7b
2ob2o6bobo5bo31b2obo3bo2bo2bo41b2obo4bo2bo7b3o38b3o4b3ob2o$146bo3bo3bo
bob2o9bo39bobo5bo39bo7b3o4bobo48b3o$144b2obo3bo2bo2bo52bo48b3o4b3ob2o$
125bo19bobo5bo105b3o$124bobo5bo13bo91b3o$123b2obo3bo2bo2bo101b3o4b3ob
2o66bo$125bo3bo3bobob2o63bo5b2o26bo7b3o4bobo68bo$128bo7b2ob2o60b2o5b2o
32b2obo4bo2bo61b2o5b2o$128bo7b2ob2o59b2o5b2o33b2obo4bo2bo61bo8bo$125bo
3bo3bobob2o62bobo3bobo26bo7b3o4bobo61bo4bobo$123b2obo3bo2bo2bo65b2o4b
4o6bo19b3o4b3ob2o65b3o3bo2bo$124bobo5bo70bo3bo2b2o5bobo5bo12b3o80bo2b
2o5b3o$125bo81bob2o5b2obo3bo2bo2bo91b3o7b3o4b3ob2o$207b3o8bo3bo3bobob
2o90bo6bo7b3o4bobo$221bo7b2ob2o101b2obo4bo2bo$221bo7b2ob2o101b2obo4bo
2bo$218bo3bo3bobob2o97bo7b3o4bobo$216b2obo3bo2bo2bo101b3o4b3ob2o$217bo
bo5bo105b3o$218bo5$141bo$140bobo5bo105b3o$139b2obo3bo2bo2bo101b3o4b3ob
2o$141bo3bo3bobob2o97bo7b3o4bobo$144bo7b2ob2o101b2obo4bo2bo$144bo7b2ob
2o101b2obo4bo2bo$141bo3bo3bobob2o97bo7b3o4bobo$139b2obo3bo2bo2bo101b3o
4b3ob2o$140bobo5bo105b3o$141bo39$175b3o111b2o$177bo112b2o$176bo112bo7$
200bo112bo$141bo59bo112b2o$140bobo5bo50b3o52b3o56b2o$139b2obo3bo2bo2bo
101b3o4b3ob2o$141bo3bo3bobob2o97bo7b3o4bobo$144bo7b2ob2o101b2obo4bo2bo
$144bo7b2ob2o101b2obo4bo2bo$141bo3bo3bobob2o97bo7b3o4bobo$139b2obo3bo
2bo2bo101b3o4b3ob2o$140bobo5bo105b3o$141bo5$218bo$217bobo5bo105b3o$
216b2obo3bo2bo2bo101b3o4b3ob2o$218bo3bo3bobob2o97bo7b3o4bobo$221bo7b2o
b2o101b2obo4bo2bo$221bo7b2ob2o101b2obo4bo2bo$218bo3bo3bobob2o97bo7b3o
4bobo$125bo90b2obo3bo2bo2bo101b3o4b3ob2o$124bobo5bo84bobo5bo12b3o90b3o
$123b2obo3bo2bo2bo81bo19b3o4b3ob2o$125bo3bo3bobob2o97bo7b3o4bobo$128bo
7b2ob2o101b2obo4bo2bo$128bo7b2ob2o101b2obo4bo2bo$125bo3bo3bobob2o97bo
7b3o4bobo$123b2obo3bo2bo2bo101b3o4b3ob2o$124bobo5bo13bo91b3o$125bo19bo
bo5bo105b3o$144b2obo3bo2bo2bo52bo48b3o4b3ob2o$146bo3bo3bobob2o9bo39bob
o5bo39bo7b3o4bobo48b3o$149bo7b2ob2o6bobo5bo31b2obo3bo2bo2bo41b2obo4bo
2bo7b3o38b3o4b3ob2o$149bo7b2ob2o5b2obo3bo2bo2bo29bo3bo3bobob2o39b2obo
4bo2bo7b3o4b3ob2o26bo7b3o4bobo$146bo3bo3bobob2o9bo3bo3bobob2o30bo7b2ob
2o31bo7b3o4bobo5bo7b3o4bobo29b2obo4bo2bo$144b2obo3bo2bo2bo14bo7b2ob2o
28bo7b2ob2o33b3o4b3ob2o14b2obo4bo2bo29b2obo4bo2bo$145bobo5bo18bo7b2ob
2o25bo3bo3bobob2o35b3o24b2obo4bo2bo23bo7b3o4bobo$146bo22bo3bo3bobob2o
25b2obo3bo2bo2bo58bo7b3o4bobo25b3o4b3ob2o$167b2obo3bo2bo2bo28bobo5bo
64b3o4b3ob2o28b3o$168bobo5bo13bo19bo71b3o19bo$169bo18b2obo111bobo5bo$
188b2obo5b3ob2o99b2obo3bo2bo2bo$189b2o3bo4b2o2b2o99bo3bo3bobob2o$193b
2o5bo4bo101bo7b2ob2o$193b2o5bo4bo101bo7b2ob2o$189b2o3bo4b2o2b2o99bo3bo
3bobob2o$188b2obo5b3ob2o99b2obo3bo2bo2bo$188b2obo111bobo5bo$190bo113bo
!

[Scorbie]

Wow. That's really nice. (And the idea seems new.) Maybe there's something even with a smaller e.f. using blinker puffers and backwards 2c/3 fuses.

[mniemiec]

If I'd thought of this earlier, I could have saved myself a lot of time and frustration!

This is very simple and elegant. I was able to understand how this works within minutes of looking at it. (Usually, trying to figure out complex constructed Life patterns is like trying to reverse-engineer a Rube Goldberg device, and gives me a headache!)

[Dean Hickerson]

Maybe there's something even with a smaller e.f. using blinker puffers and backwards 2c/3 fuses.

Good idea! If I've computed correctly, that would give e.f. 23/16. The stationary end of the pattern should be fairly easy to build, using the known 10-glider synthesis. The moving end can almost certainly be done with some combination of c/10 rakes, but maybe there's a way to do it using just copperheads with or without tagalongs. I'll see what I can find...

P.S. (next day): I ran hundreds of experiments, and found about a dozen ways for 2 copperheads to trigger the 2c/3 blinker decay. But they all left behind a bunch of debris. Adding more copperheads to clean it up wouldn't work, because the blinker puffer would run into them. I was about to give up and start looking at using c/10 rakes instead, but then one of my experiments produced a clean reaction:

Code: Select all

x = 78, y = 21, rule = B3/S23
62bo$61bobo5bo$60b2obo3bo2bo2bo$45b5o12bo3bo3bobob2o$44bo4bo15bo7b2ob
2o$49bo15bo7b2ob2o$44bo3bo13bo3bo3bobob2o$46bo13b2obo3bo2bo2bo$45b3o
13bobo5bo$45b4o13bo$45b2ob2o$3ob3ob3ob3ob3ob3ob3ob3ob3ob3ob3o4b2o2$57b
o7bob2o$56b3o5bo6bo$55bo4bo2b2o3bo2bo$42b6o6b3o4bobo5b2o$41bo5bo6b3o4b
obo5b2o$47bo7bo4bo2b2o3bo2bo$41bo4bo9b3o5bo6bo$43b2o12bo7bob2o!

[simsim314]

Adding more copperheads to clean it up wouldn't work, because the blinker puffer would run into them.

You could just send destructive *WSS together with the blinker puffer to clean the mess in front of the puffer. But your finding is great.

[Sphenocorona]

The above ideas gave me another idea: that maybe it's possible to make a sawtooth where the stationary part of the sawtooth is just a few simple still lifes. Have some copperheads set up so that if they are hit from behind, a blinker puffer escapes going backwards, with maybe a couple still lives close to the end of the blinker line. The blinker puffer would keep going until reaching a set of still life catalysts that would destroy the puffer cleanly and in doing so ignite the fuse. The fuse burns back towards the copperheads, and when it reaches the end it would interact with the junk near it to cleanly produce a spaceship heading back towards the copperheads.

[Kazyan]

The above ideas gave me another idea: that maybe it's possible to make a sawtooth where the stationary part of the sawtooth is just a few simple still lifes. Have some copperheads set up so that if they are hit from behind, a blinker puffer escapes going backwards, with maybe a couple still lives close to the end of the blinker line. The blinker puffer would keep going until reaching a set of still life catalysts that would destroy the puffer cleanly and in doing so ignite the fuse. The fuse burns back towards the copperheads, and when it reaches the end it would interact with the junk near it to cleanly produce a spaceship heading back towards the copperheads.

Ooh, nice idea. I'd like to see that, now, though the copperhead engineering would be difficult for sure.

If we allowed more complexity and simply wanted a sawtooth whose fixed point consisted only of still lifes, a loop could be created between a set of c/3 (or slower) spaceships and some Herschel circuitry, which would bounce an MWSS back and forth. A pair of c/3 rakes on the sideline could then lay down a track of blocks next to one of the MWSS lanes, which would be deleted on every loop by MWSS sparks.

[Dean Hickerson]

Maybe there's something even with a smaller e.f. using blinker puffers and backwards 2c/3 fuses.

Good idea! If I've computed correctly, that would give e.f. 23/16.

I've finished building the sawtooth. In this one, the minimal populations don't have the annoying dependence on a(n) mod 16 or whatever that some previous sawtooths had; instead the minimum repeating population (2327) occurs in every cycle.

(Usually, trying to figure out complex constructed Life patterns is like trying to reverse-engineer a Rube Goldberg device, and gives me a headache!)

This one's not quite as simple as the e.f. 3/2 sawtooth, but I don't think it'll cause any headaches.

This is the 6th sawtooth that I've built using copperheads; I hope it's the last!

Code: Select all

#C Sawtooth with expansion factor 23/16 = 1.4375
#C A group of guns produces an eastward p8 blinker puffer every 240 gens.
#C Most of them are destroyed by a glider, but sometimes one is allowed to
#C escape.  When an escaping puffer catches up with 2 c/10 copperhead
#C spaceships (with tagalongs), it is destroyed, and the line of blinkers
#C decays from east to west at 2c/3.  When all the blinkers are gone, a
#C pulsar is produced. This is destroyed by a glider from a p960 gun, and
#C the deletion of the glider allows another blinker puffer to escape.
#C
#C Let  a(0) = 0  and  a(n) = floor((23*a(n-1) + 37)/16).  Then an
#C escaping blinker puffer is produced in gen  b(n) = 960*a(n) + 318.
#C It hits the copperheads in gen  c(n) = 1200*a(n) + 631.  The pulsar
#C is produced in gen  p(n) = 1380*a(n) + 734,  usually.  (If
#C a(n) == 6 (mod 16),  then the glider prevents the pulsar from
#C forming; that happens first around gen 1422098.)
#C
#C The minimum repeating population is 2327, and occurs in gens
#C 960*a(n) + 240  for  n >= 1.
#C
#C The population is maximal around gens c(n), and is about  3*c(n)/40.
#C
#C    n    0    1    2     3     4     5     6     7      8      9
#C a(n)    0    2    5     9    15    23    35    52     77    113
#C b(n)  318 2238 5118  8958 14718 22398 33918 50238  74238 108798
#C c(n)  631 3031 6631 11431 18631 28231 42631 63031  93031 136231
#C p(n)  734 3494 7634 13154 21434 32474 49034 72494 106994 156674
#C
#C Dean Hickerson, 4/22/2016
#C
#C Credits:
#C The idea of using a blinker puffer for this sawtooth is due to 'Scorbie':
#C http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2057&start=225#p30145
#C
#C The c/10 spaceship, 'copperhead', was found by 'zdr', 3/5/2016, and its
#C tagalong by 'simeks', 3/20/2016:
#C http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2057
#C
#C The glider guns, with periods 240 and 960, are from Jason Summers's
#C updated version of Dieter Leithner and Peter Rott gun collection:
#C http://entropymine.com/jason/life/dpguns/
#C
#C The pentadecathlon-assisted MWSS synthesis was found by Bill Gosper
#C in 1992 or earlier.
#C
#C The blinker puffer was found by Robert T. Wainwright.  Its 10-glider
#C synthesis is from Mark Niemiec's website:
#C http://www.conwaylife.com/patterns/blinkerpuffer1_synth.rle
#C
#C The period 8 glider reflector was found by Noam Elkies in 1998.
#C
x = 360, y = 314, rule = B3/S23
305bo17bo$305b3o13bobo$308bo11bobo17bo$307b2o5b2o3bo2bo16b2o$314b2o4bo
bo15b2o4b2o$321bobo13b3o4b2o2b2o$310bo12bo4bobo7b2o4b2o2b2o$310bo17b2o
9b2o$309bobo17bo10bo$308b2ob2o$307bo5bo$310bo$307b2o3b2o$322bo$320b2o$
321b2o7b2o6b2o$293b2o33bo4bo2bo4bo$294bo33bo4bo2bo4bo$294bobo7b2o22bo
4bo2bo4bo$295b2o6bobo24b2o6b2o$302b3o$301b3o16bo$302b3o15bobo$303bobo
14b2o$304b2o3$300b2o$300bo24bo$288b2o8bobo22b3o$288bobo7b2o22bo$279b3o
b2o4b3o30b2o$279b4o2bo4b3o$283b2o4b3o$288bobo29bo$288b2o28b2ob2o2$317b
o5bo2$317b2obob2o$340b2o$340bo$333bo4bobo$332bobo3b2o$331bo3b2o$331bo
3b2o$309b3o19bo3b2o$309bo22bobo$310bo22bo$337b2o$318b2o17b2o$307bo10b
2o$307b3o$310bo$309b2o4$335b2obob2o$335bo5bo$299b3o34bo3bo$298bo3bo9bo
24b3o$298bo3bo8b3o10bo$299b3o8b5o9bo$309b2o3b2o$310b5o9bo$310bo3bo8bob
o$311bobo$299b3o10bo10b3o$298bo3bo33bo$298bo3bo33bo$299b3o12bo8b3o9bob
o$312b2ob2o17b2ob2o$307bo15bobo7bo5bo$306bo4bo5bo6bo11bo$306b3o24b2o3b
2o$299b2o10b2obob2o6bo$299b2o23bo4$248bobo9bo$248b2o10bobo$249bo10b2o
73b2o$335b2o$313b2o$313b2o$307b2o$307b2o$304b2o$303b3o$304b2o$307b2o5b
2o$307b2o5bobo$316bo$296bo19b2o$295b3o$294b5o$293b2o3b2o6$298b2o$298bo
$299b3o$301bo7$22b2o20bo$24bo17b3o$11b2o12bo15bo$11b2o12bo8b2o5b2o$8b
2o15bo8b2o$2o5b3o14bo$2o6b2o12b2o271bo9b2o$11b2o278b4obo8b2o6b2o6b2o$
11b2o278b3obobo14bo2bo4bo2bo$296bobo13bo2bo4bo2bo$297bo14bo2bo4bo2bo$
25b2o269b2o15b2o6b2o$25b2o9b2o3b2o253b2o$38b3o255b2o30bo25b2o$37bo3bo
285bobo24bo$38bobo285bob2o15b2o5bobo$8b2o3bo2bo3b2o17bo15b2o263b2o3b2o
b2o14bobo5b2o$8b5o4b5o3b2o28bo264b2o4bob2o13bo$8b2o3bo2bo3b2o3b2o18bob
o5bobo243b2o3b2o21bobo13bo2bo$44bo2bo5b2o245b5o23bo5bo8bo$43b2o255b2ob
2o29bobo7bobo$41b2o3bo253b2ob2o29b2o9b2o$43b2o256b3o$44bo2bo36b2o11b2o
$45bobo36b2o11bo2bo$101bo9bobo$50b2o19b2o15b2o11bo7bo3bo185b2o$51bo19b
o16b2o11bo7bo78bobo9bo99bo$51bobo5b2o8bobo25bo2bo7bo4bo74b2o10bobo94b
3o$52b2o7bo7b2o26b2o10bo79bo10b2o95bo10bo$62bo46bo3bo6b2o184b3o$62bo
18bo5bo23bobo6bobo182bo8bo$62bo18bo5bo34bo182b2o7bo$61bo20bo3bo35b2o
190bo15b2o$59b2o22b3o216b3o25b2o$302b3o$301bo3bo$300bo5bo$301bo3bo$67b
2o36b8o189b3o45b2o$68bo36bob4obo225b3o8bo$68bobo5bo28b8o221bo3bo9bo9b
2o$69b2o3bobo255bobo4bo8bo9b2o$73bobo248b2o4b2o16bo$72bo2bo248b2o4b2o
17bo$73bobo13b2o206b2o31b2o18b2o$74bobo12b2o206b2o33bobo$76bo257bo$55b
o242bo$56b2o239bobo$55b2o235b2o2bo2bo$292b2obo$50b2o244b2o$48bo2bo33bo
$47bo36bo$47bo36b3o$47bo$48bo2bo5b2o$13bo2bo4bo2bo4b2o19b2o5bobo$11b3o
2b6o2b3o2b2o28bo$13bo2bo4bo2bo34b2o2$42b3o$41b2ob2o$28bo12b2ob2o$28b2o
11b5o$27bobo10b2o3b2o2$15b2o185bo$14bobo184b3o$4b2o7bo6b2o4bo173b3obo$
4b2o7bo2bo2bo2bo2bobo173bo3bo$13bo6b3obob2o10b2o162bo3bo$14bobo6b2ob2o
10b2o5b2o156bob3o$15b2o7bob2o17bo158b3o$25bobo18b3o156bo$26bo21bo160bo
$39bo168bobo$24bo13bobo168b2o$24b3o178b2o$27bo176bobo$26b2o10b3o163bo
5b2o$38b3o162b2o5b2o$39bo121bo$159b3o$158bo$39bo118b2o$26b2obob2o5b3o$
26bo5bo5b3o$27bo3bo$28b3o$38bobo197b2ob2o$17b2o20bo189b3o5bo3b4o$17b3o
208bo2b3o3bo3b4o$19b2obo205bo3bobo2b2o$8b2o9bo2bo205bo3bobo2b2o$8b2o9b
2obo205bo2b3o3bo3b4o$17b3o209b3o5bo3b4o$17b2o219b2ob2o$11b2o$11b2o48bo
bo18bo$59bo3bo16b3o$51bo7bo19bo142b4o7bo$50b4o4bo4bo8b2o5b2o141bo3bo6b
o$49b2obobo4bo12b2o147bo12bo2bo$38b2o8b3obo2bo3bo3bo157bo3b2o5b3ob2obo
$38b2o9b2obobo6bobo157bo6b2o6b2ob2o$50b4o167bo6b2o6b2ob2o$25b2o24bo
169bo3b2o5b3ob2obo$25b2o35bo11b2o3b2o140bo12bo2bo$8b2o3b2o45bobo11b2o
3b2o141bo3bo6bo$61b2o159b4o7bo$9bo3bo62b3o$10b3o12bo50b3o$10b3o11b3o
50bo$23bobobo20b2o6b2o181b2o$23bobobo19bo2bo4bo2bo34b2o143b4o$13bo10b
3o20bo2bo4bo2bo4b2o28bo143bobo2bo17bo6bo$12b3o10bo21bo2bo4bo2bo4b2o20b
o5bobo143b2o2bobo15b2o6b2o$11bo36b2o6b2o26b2o5b2o149bobo13b3o6b3o$13bo
69b2o159b2o13b2o6b2o$10bo5bo8bo56b3o158b3o14bo6bo$10bo5bo7b3o56b2o157b
obo$11bo3bo7bobobo56b2o156b2o34bo21b2o$12b3o8bobobo57bo162bo29bobo19bo
$24b3o221bo7b2o21bobo7bo8bobo$25bo221bobo6b2o8b2o11bo2bo6b2o7b2o$65bo
180b2ob2o15b2o11bobo2b2o4b2o$65b3o177bo5bo26bobo3b2o4b3o$68bo98b2o79bo
29bo5b2o4b2o$67b2o98b2o76b2o3b2o37b2o$289bo2$13b2o261b2o$13b2o261b2o2$
245b2o$70bo93bo5bo75bo$69b3o92bo5bo72b3o$68b5o92bo3bo73bo10bo$67b2o3b
2o92b3o83b3o$68b5o178bo8bo$68bo3bo178b2o7bo$69bobo64bo123bo15b2o$70bo
65b3o137b2o$139bo$67b2o32bo36b2o141b2o$68bo32bobo177b2o$65b3o34bobo36b
o27b2o$65bo36bo2bo3b2o29b3o26bo122bo$102bobo4b2o28bo3bo26b3o117b4o$90b
2o9bobo34bob3obo27bo74b5o28bobo6bobob2o9b2o$89bobo9bo37b5o102bob3obo
27bo3bo3bo2bob3o8b2o$89bo157bo3bo18b2o12bo4bobob2o$88b2o158b3o19b2o8bo
4bo4b4o$120b2o121b2o4bo34bo7bo$121bo120bo2bo34bo3bo$121bobo5bo115bo34b
obo$122b2o5b2o114bo$130b2o107bo3bobo$130b3o105bo3bobo$73b2o55b2o106bo
4bo$71bo2bo54b2o108b4o$70bo58bo$70bo52b2o$70bo52b2o$64b2o5bo2bo$63bobo
7b2o17b2o4bo2bo4bo2bo$63bo28b2o2b3o2b6o2b3o$62b2o34bo2bo4bo2bo44b2o$
153b3o$150bob2o$150bo2bo$120b2o3b2o23bob2o$63bobo10b2o3b2o37b2o3b2o18b
2o6b3o$61bo3bo11b5o54b2o6bobo7b2o17b2o4bo2bob2obo2bo$61bo15b2ob2o40b3o
3b3o6b2o5bo28b2o3b2o2bo4bo2b2o$60bo4bo11b2ob2o15b2o9b2o12b3o5bo5bo6b2o
34bo2bob2obo2bo$61bo16b3o16bobo7bobo13bo5bo$61bo3bo6b2o17bo5bo8bo10b2o
$30bobo2bobo6b2o17bobo6bobo15bobo13bo2bo7b2o18bo$26b2obo2bo2bo2bob2o2b
2o28bo14bob2o13bo29bobo$30bobo2bobo19b3o14b2o12b2ob2o14bobo25bo3bo$57b
3o29bob2o15b2o25bo3bo17b2o3b2o$56bo3bo17b2o5b2o3bobo31b3o8bo3bo$55bo5b
o16b2o4bobo4bo32b3o8bo3bo18bo3bo26b2o$56bo3bo23bo38bo3bo7bo3bo19b3o25b
o2bo7bo$57b3o23b2o50bo3bo19b3o10bo13bo7b2o3bo$122b2o3b2o7bobo31b4o12bo
6bo5bo$137bo26b2o3bobob2o11bo7b5o$29bobo125b2o5b2o2bo2bob3o11bo2bo$28b
o2bo126bo10bobob2o14b2o$19b2o6b2o13b2o111b3o12b4o$19b2o4b2o3bo11bobo
110bo16bo$27b2o16bo7b2o$28bo2bo10bo2bo7b2o5b2o$29bobo13bo14bo$42bobo
16b3o$42b2o19bo61b2o$125b2o!

[simsim314]

This is the 6th sawtooth that I've built using copperheads; I hope it's the last!

And a nice one!

How about using constructible ships, like demonoid or cateloopillar?

[Kazyan]

And a nice one!

How about using constructible ships, like demonoid or cateloopillar?

Ouch, getting the gun periods to work out would be a nightmare.

Another option is to use a faster fuse than 2/3c. Unfortunately, there don't seem to be any easy constructible puffers for lightspeed fuses. A long string of beehives would work:

Code: Select all

x = 137, y = 104, rule = B3/S23
18b2o$2b2o13b2ob2o$b4o13b4o$2ob2o14b2o$b2o3$15b2o4bo$4b2o9b2o3b3o7bo$
3bo2bo12b2ob2o4b2o$2b2o2bo11b3ob3o4b2o$3b2o2bo11b2ob3o$4b4o12bobo$35bo
$33b2o$2b2o30b2o$b4o4b4o$2ob2o4bo3bo$b2o6bo30bo$10bo2bo24b2o$39b2o3$
45bo$43b2o$44b2o3$13b4o5b2o26bo$13bo3bo3b2ob2o22b2o$13bo8b4o23b2o$14bo
2bo5b2o2$18bo9b2o25bo$16b3o8b5o21b2o$15bo3bo5bo4b2o22b2o$15bo4b5o5b2o$
15b2obob4o4b2o$17bo3b2ob3o33bo$18bobo37b2o$59b2o$40bo$13b4o24b2o$13bo
3bo22b2o23bo$13bo17b4o28b2o$14bo2bo13bo3bo28b2o$31bo23bo$32bo2bo20b2o$
55b2o2$69b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o$63bo
4bo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2b
o$63b2o4b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o$62bobo
$67bo$66b2o$31b4o13bo17bobo$31bo3bo12b2o$13b4o14bo15bobo$13bo3bo14bo2b
o26bo$13bo47b2o$14bo2bo43bobo$34b3o$18bo10bobobo3bo$16b3o10bo7bo19bo$
15bo3bo15b2o19b2o$15bo4b3o33bobo$15b2obob3o8bo$17bo3b2o$18bobo31bo$51b
2o$51bobo$13b4o5b2o$13bo3bo3b2ob2o$13bo8b4o21bo$14bo2bo5b2o21b2o$46bob
o3$42bo$41b2o$41bobo2$2b2o$b4o4b4o24bo$2ob2o4bo3bo22b2o$b2o6bo26bobo$
10bo2bo2$14b2o16bo$4b2o8b2o15b2o$3bo2bo5bo3bo14bobo$2b2o2bo4bo3bo$3b2o
2bo2bo4bo$4b4o3bobo13bo$26b2o$26bobo$2b2o$b4o$2ob2o$b2o15b2o$17b2ob2o$
18b4o$19b2o!

...but that's still thorny to make a sawtooth out of.

[simsim314]

Ouch, getting the gun periods to work out would be a nightmare.

I've built a while back a universal logarithmic gun script for any period above 8K. It works well if you need compact high period gun.

Here it's for Demonoid period 438,852:

Code: Select all

x = 882, y = 758, rule = B3/S23
749bo$709b2o38b3o$710bo41bo14bo$710bobo38b2o12b3o$711b2o2b2o47bo$715b
2o47b2o3$763b2o$744b2o17b2o$744b2o6$709b2o36b2o$708bobo16b2o19bo$708bo
18bobo15b3o$707b2o20bo15bo$723b2o4b2o19b2o$723bobo25bo$725bo22b3o$716b
2o7b2o21bo$716b2o7$706b2o$707bo$707bobo$708b2o$724bo$722b3o$721bo$721b
2o28b2o$750bobo$750bo29b2o$749b2o29bobo$689b2o91bo$666bo23bo64b2o25b2o
$664b3o23bobo61bobo4b2o$663bo27b2o61bo7bo$663b2o88b2o4b3o$759bo$640bo
42bo83b2o$640b3o38b3o44b2o36bobo$633bo9bo36bo47b2o36bo$633b3o6b2o23b2o
11b2o83b2o$636bo30b2o$635b2o$723b2o$723b2o$727b2o54b2o$727b2o54bobo$
785bo$785b2o$692b2o27b2o$631bo23b2o35b2o11b2o14b2o$505b2o3b2o118bobo
22bo49bo$503b3obo2b2o119bo14b2o8b3o47b3o$502bo4bo138bo11bo49bo$502bo2b
2ob4o135b3o$501b2obobobo2bo137bo125b2o$502bobobobo257b2o7b2o$502bobob
2o125b2o32b2o98bo$503bo128bobo33bo98bobo$632bo32b3o100b2o$516b2o113b2o
32bo85bo32b2o$507b2o7bo130b2o100b3o32bo$507b2o5bobo130bobo52b2o21bo22b
o33bobo$514b2o133bo52b2o21b3o20b2o32b2o$640b2o7b2o40b2o35bo$640b2o50bo
34b2o38bo$692bobo72b3o$693b2o63bo11bo$758b3o8b2o14bo$761bo22bobo$504b
2o254b2o23bo$505bo$502b3o125b2o58b2o25b2o$502bo128bo59bo25b2o$631bobo
57bobo$632b2o58b2o3$705b2o$705bobo6b2o32b2o$650b2o55bo6bo20b2o11b2o23b
2o23bo$650bo56b2o6b3o18bo36bo22b3o$648bobo66bo15b3o38b3o18bo$648b2o83b
o42bo18b2o$536bo$518b2o14b5o213b2o$519bo13bo5bo213bo49b2ob2o$519bobo
12b3o2bo163b2o45b3o51bob2o$520b2o15bob2o162bobo44bo53bo$534b4o2bo164bo
90b2o4b3o$529b2o3bo3b2o165b2o89b2o3bo3b2o$529b2o4b3o263b4o2bo$537bo
249b2o15bob2o$537bob2o245bobo12b3o2bo$536b2ob2o245bo13bo5bo$630b2o15b
2o38b2o96b2o14b5o$629bobo15b2o37bobo114bo$528b2o99bo25b2o29bo25b2o129b
2o$528bo99b2o25bo29b2o25bo131bo$529b3o121bobo37b2o15bobo131bobo$531bo
121b2o38b2o15b2o133b2o$870b2o$870b2o2$838bo$635b2o199b3o$636bo183bo14b
o$591bo44bobo181b3o12b2o$589b3o45b2o184bo$588bo233b2o$588b2o2$565bo42b
o83b2o129b2o$565b3o38b3o15bo66bobo129b2o17b2o$558bo9bo36bo18b3o6b2o56b
o150b2o$558b3o6b2o23b2o11b2o20bo6bo55b2o$561bo30b2o32b2o6bobo243b2o$
560b2o73b2o243b2o3$648b2o58b2o129b2o$648bobo57bobo128bo19b2o$623b2o25b
o59bo40bo88b3o15bobo$623b2o25b2o58b2o39b3o88bo15bo$754bo81b2o19b2o$
556bo23b2o171b2o81bo$555bobo22bo256b3o$556bo14b2o8b3o62b2o191bo$571bo
11bo62bobo93b2ob2o$572b3o55b2o16bo93b2obo$574bo38b2o16bo16b2o50b2o43bo
$613bo14b3o6bo53b2o7b2o43b3o4b2o$558b2o32b2o20b3o11bo7bobo53bo50b2o3bo
3b2o$557bobo33bo22bo20bo54bobo47bo2b4o96b2o$557bo32b3o100b2o47b2obo15b
2o82bo$556b2o32bo85bo32b2o32bo2b3o12bobo62b2o15bobo$572b2o100b3o32bo
33bo5bo13bo62b2o15b2o$572bobo52b2o21bo22bo33bobo34b5o14b2o$574bo52b2o
21b3o20b2o32b2o37bo$565b2o7b2o40b2o35bo$565b2o50bo34b2o38bo$617bobo72b
3o$618b2o63bo11bo$683b3o8b2o14bo$686bo22bobo$685b2o23bo2$555b2o58b2o
25b2o$556bo59bo25b2o181b2o$556bobo57bobo205bobo$557b2o58b2o205bo$823b
2o2$630b2o73b2o$630bobo6b2o32b2o30bo$575b2o55bo6bo20b2o11b2o23b2o6b3o$
575bo56b2o6b3o18bo36bo9bo$573bobo66bo15b3o38b3o82b2o$573b2o83bo42bo82b
2o2$677b2o156b2o$678bo156b2o$628b2o45b3o93b2o$628bobo44bo96bo$630bo
141bobo$630b2o141b2o2$824b2o$825bo19b2o5b2o$791b2o32bobo17bo6bo$555b2o
15b2o38b2o177b2o15bo17b2o15bobo7b3o$554bobo15b2o37bobo192b3o29bo4b2o
10bo$554bo25b2o29bo25b2o134b2o30bo31bobo$553b2o25bo29b2o25bo134bobo30b
2o30bobo$578bobo37b2o15bobo134bo53b2o10bo$578b2o38b2o15b2o134b2o52bobo
$825bo$824b2o$839b2o$782b2o55bo$560b2o219bobo56b3o$561bo219bo60bo$516b
o44bobo216b2o$514b3o45b2o$513bo$513b2o2$490bo42bo83b2o183b2o$490b3o38b
3o15bo66bobo183bobo$483bo9bo36bo18b3o6b2o56bo187bo$483b3o6b2o23b2o11b
2o20bo6bo55b2o187b2o$486bo30b2o32b2o6bobo$485b2o73b2o3$573b2o58b2o$
573bobo57bobo$548b2o25bo59bo$548b2o25b2o58b2o2$481bo23b2o$480bobo22bo$
481bo14b2o8b3o62b2o$496bo11bo62bobo$497b3o55b2o16bo$499bo38b2o16bo16b
2o50b2o$538bo14b3o6bo53b2o7b2o$483b2o32b2o20b3o11bo7bobo53bo225b2o$
482bobo33bo22bo20bo54bobo224bo$482bo32b3o100b2o224bobo$481b2o32bo85bo
32b2o209b2o$497b2o100b3o32bo235b2o$497bobo52b2o21bo22bo33bobo235b2o$
499bo52b2o21b3o20b2o32b2o$490b2o7b2o40b2o35bo259bo$490b2o50bo34b2o38bo
218b3o$542bobo72b3o200bo14bo$543b2o63bo11bo199b3o12b2o$608b3o8b2o14bo
187bo$611bo22bobo185b2o$610b2o23bo2$480b2o58b2o25b2o254b2o$481bo59bo
25b2o254b2o17b2o$481bobo57bobo298b2o$482b2o58b2o$880b2o$880b2o$555b2o
73b2o$555bobo6b2o32b2o30bo$500b2o55bo6bo20b2o11b2o23b2o6b3o205b2o$500b
o56b2o6b3o18bo36bo9bo205bo19b2o$498bobo66bo15b3o38b3o213b3o15bobo$498b
2o83bo42bo215bo15bo$836b2o19b2o$602b2o232bo$603bo233b3o$553b2o45b3o
236bo$553bobo44bo$555bo$555b2o3$845b2o$845bo$480b2o15b2o38b2o287b2o15b
obo$479bobo15b2o37bobo287b2o15b2o$479bo25b2o29bo25b2o$478b2o25bo29b2o
25bo$503bobo37b2o15bobo$503b2o38b2o15b2o5$485b2o$486bo$441bo44bobo$
439b3o45b2o336b2o$438bo385bobo$438b2o384bo$823b2o$415bo42bo83b2o$415b
3o38b3o15bo66bobo$408bo9bo36bo18b3o6b2o56bo$408b3o6b2o23b2o11b2o20bo6b
o55b2o$411bo30b2o32b2o6bobo$410b2o73b2o3$498b2o58b2o275b2o$498bobo57bo
bo274b2o$473b2o25bo59bo$473b2o25b2o58b2o2$406bo23b2o$405bobo22bo$406bo
14b2o8b3o62b2o326b2o$421bo11bo62bobo326bo19b2o5b2o$422b3o55b2o16bo326b
obo17bo6bo$424bo56bo16b2o50b2o274b2o15bobo7b3o$478b3o6bo53b2o7b2o286bo
4b2o10bo$408b2o32b2o34bo7bobo53bo294bobo$407bobo33bo43bo54bobo292bobo$
407bo32b3o100b2o281b2o10bo$406b2o32bo85bo32b2o264bobo$422b2o100b3o32bo
265bo$120b2o300bobo52b2o21bo22bo33bobo264b2o$120b2o302bo52b2o21b3o20b
2o32b2o280b2o$415b2o7b2o40b2o35bo335bo$415b2o50bo34b2o38bo297b3o$467bo
bo72b3o297bo$468b2o63bo11bo$533b3o8b2o14bo$536bo22bobo$535b2o23bo2$
105b2o298b2o58b2o25b2o$105b2o299bo59bo25b2o$406bobo57bobo$407b2o58b2o
3$480b2o73b2o$480bobo6b2o32b2o30bo$425b2o55bo6bo20b2o11b2o23b2o6b3o$
425bo56b2o6b3o18bo36bo9bo$423bobo66bo15b3o38b3o$125b2o296b2o83bo42bo$
125bo$126b3o398b2o$128bo47b2o350bo$176bo301b2o45b3o$174bobo301bobo44bo
$174b2o304bo$480b2o5$405b2o15b2o38b2o$404bobo15b2o37bobo$137bo34bo231b
o25b2o29bo25b2o$137b3o32b3o228b2o25bo29b2o25bo$140bo34bo252bobo37b2o
15bobo$117b2o20b2o33b2o252b2o38b2o15b2o$117b2o7b2o56b2o$126bo57bo$124b
obo55bobo$124b2o4b2o44b2o4b2o$108b2o20bo44bo2bo231b2o$109bo18bobo45b2o
233bo$109bobo16b2o34b2o200bo44bobo$110b2o52b2o198b3o45b2o$363bo$363b2o
2$340bo42bo83b2o$340b3o38b3o15bo66bobo$333bo9bo36bo18b3o6b2o56bo$333b
3o6b2o23b2o11b2o20bo6bo55b2o$139b2o32b2o3b2o156bo30b2o32b2o6bobo$139b
2o11b2o20bo3bo156b2o73b2o$152bo18b3o5b3o$116b2o35b3o15bo9bo$112b2o2b2o
37bo267b2o58b2o$111bobo309bobo57bobo$111bo286b2o25bo59bo$110b2o286b2o
25b2o58b2o2$331bo23b2o$203bo126bobo22bo$203b3o125bo14b2o8b3o62b2o$141b
2o63bo139bo11bo62bobo$141bo63b2o140b3o55b2o16bo$142b3o204bo56bo16b2o
50b2o$144bo258b3o6bo53b2o7b2o$333b2o32b2o34bo7bobo53bo$332bobo33bo43bo
54bobo$332bo32b3o100b2o$331b2o32bo85bo32b2o$215b2o130b2o100b3o32bo$
208b2o5bobo129bobo52b2o21bo22bo33bobo$208b2o7bo131bo52b2o21b3o20b2o32b
2o$217b2o121b2o7b2o40b2o35bo$340b2o50bo34b2o38bo$204bo187bobo72b3o$
203bobob2o184b2o63bo11bo$203bobobobo248b3o8b2o14bo$202b2obobobo2bo248b
o22bobo$203bo2b2ob4o247b2o23bo$39bo163bo4bo$39b3o162b3obo2b2o117b2o58b
2o25b2o$42bo163b2o3b2o118bo59bo25b2o$41b2o288bobo57bobo$56b2o274b2o58b
2o$56bo$54bobo$43bo10b2o349b2o73b2o$24bo17bobo360bobo6b2o32b2o30bo$24b
3o15bobo305b2o55bo6bo20b2o11b2o23b2o6b3o$27bo9b2o4bo306bo56b2o6b3o18bo
36bo9bo$26b2o8bobo15b2o292bobo66bo15b3o38b3o$36bo17bobo165bo125b2o83bo
42bo$35b2o19bo163b5o14b2o$56b2o161bo5bo13bo212b2o$219bo2b3o12bobo213bo
$218b2obo15b2o164b2o45b3o$218bo2b4o178bobo44bo$219b2o3bo3b2o175bo$221b
3o4b2o175b2o$45b2o174bo$45b2o171b2obo$218b2ob2o2$330b2o15b2o38b2o$229b
2o98bobo15b2o37bobo$230bo98bo25b2o29bo25b2o$227b3o98b2o25bo29b2o25bo$
227bo125bobo37b2o15bobo$353b2o38b2o15b2o$57b2o$57bo$55bobo$55b2o$335b
2o$336bo$291bo44bobo$289b3o45b2o$288bo$288b2o2$68b2o195bo42bo83b2o$68b
o196b3o38b3o15bo66bobo$66bobo199bo36bo18b3o6b2o56bo$66b2o199b2o23b2o
11b2o20bo6bo55b2o$37b2o15b2o236b2o32b2o6bobo$36bobo15b2o279b2o$36bo$
35b2o$348b2o58b2o$348bobo57bobo$323b2o25bo59bo$323b2o25b2o58b2o2$42bo
213bo23b2o$42b3o210bobo22bo$45bo210bo14b2o8b3o62b2o$23b2o19b2o225bo11b
o62bobo$23bo15bo232b3o55b2o16bo$21bobo15b3o232bo38b2o16bo16b2o50b2o$
21b2o19bo270bo14b3o6bo53b2o7b2o$41b2o215b2o32b2o20b3o11bo7bobo53bo$
257bobo33bo22bo20bo54bobo$257bo32b3o100b2o$2o254b2o32bo85bo32b2o$2o
270b2o100b3o32bo$272bobo52b2o21bo22bo33bobo$38b2o234bo52b2o21b3o20b2o
32b2o$38b2o17b2o206b2o7b2o40b2o35bo$57b2o206b2o50bo34b2o38bo$317bobo
72b3o$318b2o63bo11bo$58b2o323b3o8b2o14bo$58bo327bo22bobo$45b2o12b3o
323b2o23bo$46bo14bo$43b3o209b2o58b2o25b2o$43bo212bo59bo25b2o$256bobo
57bobo$10b2o245b2o58b2o$10b2o2$330b2o73b2o$330bobo6b2o32b2o30bo$275b2o
55bo6bo20b2o11b2o23b2o6b3o$275bo56b2o6b3o18bo36bo9bo$273bobo66bo15b3o
38b3o$273b2o83bo42bo2$377b2o$378bo$328b2o45b3o$328bobo44bo$330bo$330b
2o5$255b2o15b2o38b2o$254bobo15b2o37bobo$254bo25b2o29bo25b2o$253b2o25bo
29b2o25bo$278bobo37b2o15bobo$278b2o38b2o15b2o5$260b2o$261bo$261bobo$
262b2o4$317b2o$249bo66bobo$249b3o6b2o56bo$252bo6bo55b2o$251b2o6bobo$
260b2o$221bo$220bobo$220bobo50b2o58b2o$221bo51bobo57bobo$248b2o25bo59b
o$248b2o25b2o58b2o4$271b2o$271bobo$255b2o16bo$238b2o16bo16b2o50b2o$
238bo14b3o6bo53b2o7b2o$239b3o11bo7bobo53bo$241bo20bo54bobo$318b2o$301b
o32b2o$299b3o32bo$252b2o21bo22bo33bobo$252b2o21b3o20b2o32b2o$241b2o35b
o$242bo34b2o38bo$242bobo72b3o$243b2o63bo11bo$308b3o8b2o14bo$311bo22bob
o$310b2o23bo2$240b2o25b2o$241bo25b2o$241bobo$242b2o3$255b2o73b2o$255bo
bo6b2o32b2o30bo$257bo6bo20b2o11b2o23b2o6b3o$257b2o6b3o18bo36bo9bo$267b
o15b3o38b3o$283bo42bo2$302b2o$303bo$253b2o45b3o$253bobo44bo$255bo$255b
2o3$281b2o3b2o$279b3obo2b2o$237b2o39bo4bo$236bobo39bo2b2ob4o$236bo25b
2o13b2obobobo2bo$235b2o25bo15bobobobo$243b2o15bobo15bobob2o$243b2o15b
2o17bo2$292b2o$283b2o7bo$283b2o5bobo$290b2o7$242b2o36b2o$241bobo37bo$
241bo36b3o$240b2o36bo2$280b2o3b2o$280b2o2bob3o$284bo4bo$280b4ob2o2bo$
280bo2bobobob2o$283bobobobo$284b2obobo$252b2o34bo$252b2o$264b2o8b2o$
264bobo8bo7b2o$266bo8bobo5b2o$266b2o8b2o2$241b2o$242bo19b2o$242bobo17b
o56bo$243b2o15bobo38b2o14b5o$247b2o6bo4b2o40bo13bo5bo$246bo2bo4bobo29b
2o14bobo12b3o2bo$247b2o5bobo29bo16b2o15bob2o$243b2o10bo31b3o27b4o2bo$
242bobo44bo22b2o3bo3b2o$242bo69b2o4b3o$241b2o77bo$256b2o62bob2o$256bo
62b2ob2o$257b3o$259bo$275b2o34b2o$276bo34bo$276bobo33b3o$277b2o2b2o31b
o5bo$281b2o35b3o15bo9bo$317bo18b3o5b3o$304b2o11b2o20bo3bo$304b2o32b2o
3b2o5$343bo$342bo$342b3o$217bo57b2o52b2o$215b5o14b2o38bobo16b2o34b2o$
214bo5bo13bo39bo18bobo45b2o$214bo2b3o12bobo38b2o20bo44bo2bo$213b2obo
15b2o55b2o4b2o44b2o4b2o$213bo2b4o69bobo55bobo$214b2o3bo3b2o66bo57bo$
216b3o4b2o57b2o7b2o56b2o$216bo65b2o20b2o33b2o$213b2obo88bo34bo$213b2ob
2o84b3o32b3o$302bo34bo2$224b2o$225bo$222b3o47b2o$222bo50bo$273bobo$
274b2o2$226bo$224b3o$223bo69bo$223b2o66b3o$290bo$290b2o5$213b2o$212bob
o5b2o47b2o$212bo7b2o48bo$211b2o57bobo64b2o$271b2o65bo$225bo39bo72bobo$
221b2obobo38b3o71b2o2b2o37bo$220bobobobo41bo74b2o35b3o15bo9bo$217bo2bo
bobob2o39b2o110bo18b3o5b3o$217b4ob2o2bo139b2o11b2o20bo3bo$221bo4bo139b
2o32b2o3b2o$217b2o2bob3o$217b2o3b2o3$277b2o6b2o$270b2o5bobo5b2o$270b2o
7bo$279b2o56b2o52b2o$336bobo16b2o34b2o$266bo69bo18bobo45b2o$265bobob2o
64b2o20bo44bo2bo$265bobobobo79b2o4b2o44b2o4b2o$264b2obobobo2bo76bobo
55bobo$265bo2b2ob4o78bo57bo$265bo4bo73b2o7b2o56b2o$266b3obo2b2o53bo15b
2o20b2o33b2o$268b2o3b2o53b3o36bo34bo$331bo32b3o32b3o$330b2o32bo34bo6$
399b2o$399bobo$401bo$401b2o2$355bo$353b3o$352bo$352b2o10$332b2o81bo$
332b2o79b3o$412bo$412b2o7$347b2o53b2o$347b2o52bobo5b2o$401bo7b2o$400b
2o2$414bo$410b2obobo$409bobobobo$406bo2bobobob2o$406b4ob2o2bo$410bo4bo
$406b2o2bob3o$406b2o3b2o17$127b2o3b2o2b2obo6b2obo6b2obo6b2obo6b2obo$
127b2o3b2o2bob2o6bob2o6bob2o6bob2o6bob2o$140b2o2b2o4b2o2b2o4b2o2b2o14b
2o$127b2o3b2o6bo3bo5bo3bo5bo3bo15bo$127bobobobo7bo3bo5bo3bo5bo3bo15bo$
129bobo8b2o2b2o4b2o2b2o4b2o2b2o14b2o$128b2obo4b2obo6b2obo6b2obo6b2obo
6b2obo$132b2o2bob2o6bob2o6bob2o6bob2o6bob2o$133bo6b2o2b2o4b2o2b2o4b2o
8b2o2b2o$132bo7bo3bo5bo3bo5bo9bo3bo$132b2o7bo3bo5bo3bo5bo9bo3bo$133bo
6b2o2b2o4b2o2b2o4b2o8b2o2b2o$132bo3b2obo6b2obo6b2obo6b2obo6b2obo$132b
2o2bob2o6bob2o6bob2o6bob2o6bob2o!

[codeholic]

The period of the gun has to be different because of Doppler effect.