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Thread For Your Useless Discoveries

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Re: Thread For Your Useless Discoveries

Postby NotAvailableCooper » August 18th, 2014, 7:30 pm

Phi spark moves a block over two spaces as it dissipates. Kinda fun to watch.

x = 6, y = 9, rule = B3/S23
3bo$2b3o$bobobo$bobobo$2b3o$3bo2$2o$2o!
Methuselahs unbound.
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Re: Thread For Your Useless Discoveries

Postby NotAvailableCooper » August 19th, 2014, 4:59 pm

Modified Pipsquirter 2 extends Pentoad reaction by 2 generations with sparks.

x = 31, y = 36, rule = B3/S23
23bo2bo2bo$20bo2b7o$20b3o$24bob2o$22b3o3bo$21bo4bobo$20bob2obo2b2o$20b
obo3bobo$19b2o2bob2obo$21bobo4bobo$21bobobobob2o$20b2obobobo$9b2o11bo
4bo$5b2obobo11bobob2ob2o$5b2obobob2o7b2obo3bobo$8bo2bo3bo8b4o$8bo7bob
2o2b2o$3bo2bob2o6bo7b4o$3b4o7bo6b2obo2bo$7b2o2b2obo7bo$3b4o8bo3bo2bo$o
bo3bob2o7b2obobob2o$2ob2obobo11bobob2o$3bo4bo11b2o$3bobobob2o$2obobobo
bo$obo4bobo$2bob2obo2b2o$2bobo3bobo$b2o2bob2obo$2bobo4bo$2bo3b3o$3b2ob
o$8b3o$b7o2bo$bo2bo2bo!
Methuselahs unbound.
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Re: Thread For Your Useless Discoveries

Postby pi_guy314 » September 2nd, 2014, 4:20 pm

Here's a 3 glider collision that creates a dead spark coil after 119 gen.

#CXRLE Pos=1,-8
x = 9, y = 12, rule = B3/S23
7bo$6bo$6b3o6$b2o$obob2o$2bobobo$4bo!
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Re: Thread For Your Useless Discoveries

Postby mniemiec » September 2nd, 2014, 9:20 pm

pi_guy314 wrote:Here's a 3 glider collision that creates a dead spark coil after 119 gen.

I was wondering why this has never been reported before, until I examined the starting position more closely. The two bottom gliders could not have reached this position unless they were created there - they would normally have interacted two generations earlier. When running collisions of multiple gliders, it's often a good idea to move them back a bit to ensure that they don't hit earlier than expected. (For example, in my glider synthesis expert system, all the recipes are created with the gliders moved back 25 squares - i.e. 100 generations - to avoid similar surprises.)
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Re: Thread For Your Useless Discoveries

Postby BobShemyakin » September 4th, 2014, 1:20 pm

Zoo.
Birds in a cage (the objects in a confined space)
I've been wanting to know the behavior of living objects (birds) in the space defined by a fixed boundary (cage).
Here are same birds in cages, which I found.
x = 308, y = 136, rule = B3/S23
36bo18b2o18b2o19b2o15b2o2b2o16b2o2b2o2b2o15b2o2b2o19b2o2b2o19b2o2b2o2b
2o15b2ob2o2b2o$35bobo17b2o18b2o19b2o15b2o2b2o16b2o2b2o2b2o15b2o2b2o19b
2o2b2o19b2o2b2o2b2o15b2ob2o2b2o$5b2obo27bo$5bob2o44b6o14b6o15b4o15b8o
12b14o11b10o15b10o15b12o13b11o$9b2o23b5o13bo6bo12bo6bo13bo4bo13bo8bo7b
2obo5bo2bo5bob2o6bo3bo6bo13bo6bo3bo10b2obobo8bobo11bo11bo$9bo23bo3bobo
12bo2b3obo12bob4obo9b2o2bob2obo2b2o9bo2b5obo7b2obo2b2o6b2o2bob2o6bob2o
b2ob2obo13bobo3bob2obo10b2ob2o2b2o2b2o2b2o11bo3b2ob2o3bo$10bo19bo2bo4b
2o2bo6b2obobo2bobob2o6b2obobo2bobob2o6bobobo2bobobobo6b2obobo4bobob2o
7bobob8obobo6b2obob2ob2ob2obob2o7b2obob2ob4o2bob2o10bo4bo2bo4bob2o5b2o
bo4bobo4bob2o$9b2o18bobobo5bobobo5b2obobo4bob2o6b2obobo4bob2o8bobo4bob
o8b2obo2bo2bo2bob2o4b2obob2o8b2obob2o3b2obo9b2ob2o7b2ob2obo7bob2o10bob
o8bobob2o5b2obobo2bobo2bobob2o$5b2obo21bo2b2o4bo2bo9bob2o3bo12bob2o3bo
9bobobo2bobobobo9b2ob4ob2o7b2obobob8obobob2o6bob2ob2ob2obo13bob2ob2obo
2bo10b2obob2o6b2obo11bob3o3b3obo$5bob2o24bobo3bo12bo6bo12bo6bo9b2o2bob
2obo2b2o6b2obo2bo2bo2bob2o7bo2b2o6b2o2bo9bob2ob2ob2obo13bo2bob2ob2obo
10b2obo12bo8b2obo11bob2o$3b2o29b5o14b6o14b6o14bo4bo10b2obobo4bobob2o7b
o5bo2bo5bo6b2ob2o9bob2o7b2obo7bob2ob2o10bo12bob2o5b2obob3o3b3obob2o$3b
o90b4o14bob2o2b2obo11b14o7b2obob2ob2ob2obob2o7b2obo2b4ob2obob2o10bob2o
6b2obob2o8bobo2bobo2bobo$4bo31bo18b2o18b2o35bo8bo35bob2ob2ob2obo13bob
2obo3bobo10b2obobo8bobo11bo4bobo4bo$3b2o30bobo17b2o18b2o17b2o17b8o14b
2o2b2o2b2o12bo6bo3bo13bo3bo6bo10b2obo4bo2bo4bo8b2obo3b2ob2o3bob2o$5b2o
bo27bo57b2o39b2o2b2o2b2o13b10o15b10o14b2o2b2o2b2o2b2ob2o5b2obo11bob2o$
5bob2o104b2o2b2o88bobo8bobob2o9b11o$113b2o2b2o41b2o2b2o19b2o2b2o17b12o
$160b2o2b2o19b2o2b2o42b2ob2o2b2o$208b2o2b2o2b2o15b2ob2o2b2o$208b2o2b2o
2b2o6$4b2obo27b2o18b2o2b2o14b2ob2o15b2o2b2o2b2o15b2ob2o2b2o16b2ob2o2b
2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o
2b2o$4bob2o27b2o18b2o2b2o14b2ob2o15b2o2b2o2b2o15b2ob2o2b2o16b2ob2o2b2o
16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b2o16b2ob2o2b
2o$8b2o$8bo24b6o14b8o12b9o11b12o13b11o14b11o14b11o14b11o14b11o14b11o
14b11o14b11o$9bo22bo6bo12bo8bo7b2obobo2bo2bobo6b2obo3bo8bo8b2obo9bobo
9b2obo3bo7bo9b2obo2bo6bobo9b2obo11bo9b2obo11bo9b2obo11bo9b2obo11bo9b2o
bo11bo$8b2o22bo2b2o2bo12bob2o2b2obo7b2obo9bo6b2obob2o4bob2obo8b2ob2o2b
ob2o4bo9b2obobo3b2ob2obo9b2ob2o3bob2o3bo9b2obo2bobob3o2bo9b2obob2obob
4obo9b2obob2ob2o2b2obo9b2obo2bob2ob2o2bo9b2obob2ob2ob3obo$4b2obo21b2ob
obo2bobob2o6b2obob2o2bo2bob2o7bo9bob2o6bob2o3b2ob2obob2o8bo3b2obo4bob
2o9bob4obobo2bob2o9bo3b2obo3b2ob2o9bobob2obo2bobob2o9bobob2obo2bobob2o
9bobob2obo2bobob2o9bobob2obo2bobob2o9bobob2obo2bobob2o$4bob2o21b2obobo
2bobob2o6b2ob2o7bob2o4b2obo2bo3bo2bob2o6bo11b2ob2o8bo6bob2obob2o9bo6bo
bob2ob2o9bobo4bobo2bob2o9bobo4bobo2bob2o9bobo4bobo2bob2o9bo6bobo2bob2o
9bobo4bobo2bob2o9bobo4bobo2bob2o$8b2o22bobo2bobo12bo8bo7b2obob2o3b2obo
6b2obob2o9bo8b2obob4obobo2bo9b2obob4obobo2bo9b2obob4obob2obo9b2obob4ob
ob2obo9b2obob4obob2obo9b2obo2b3obob2obo9b2obo2b3obob2obo9b2obo2b3obob
2obo$8bo20b2obo6bob2o6b2obo7b2ob2o7bo9bob2o3b2obo2bo9bo8b2obobo7bobob
2o6b2obobo7bobob2o6b2obo11bob2o6b2obo11bob2o6b2obo11bob2o6b2obobo7bobo
b2o6b2obobo7bobob2o6b2obobo7bobob2o$9bo19b2ob2o4b2ob2o6b2obo2bo2b2obob
2o7bob2o3b2obob2o6bo9bo2bob2o8bo2bobob4obob2o9bo2bobob4obob2o9bob2obob
4obob2o9bob2obob4obob2o9bob2obob4obob2o9bob2obob3o2bob2o9bob2obob3o2bo
b2o9bob2obob3o2bob2o$8b2o22bo6bo12bob2o2b2obo7b2obo2bo3bo2bo9bo9b2obob
2o5b2obob2obo6bo9b2ob2obobo6bo9b2obo2bobo4bobo9b2obo2bobo4bobo9b2obo2b
obo4bobo9b2obo2bobo6bo9b2obo2bobo4bobo9b2obo2bobo4bobo$4b2obo24bobo2bo
bo12bo8bo7b2obo9bo6b2ob2o11bo8b2obo4bob2o3bo9b2obo2bobob4obo9b2ob2o3bo
b2o3bo9b2obobo2bob2obobo9b2obobo2bob2obobo9b2obobo2bob2obobo9b2obobo2b
ob2obobo9b2obobo2bob2obobo$4bob2o25b6o14b8o11bo9bob2o3b2obob2ob2o3b2ob
o11bo4b2obo2b2ob2o9bob2ob2o3bobob2o9bo3b2obo3b2ob2o9bo2b3obobo2bob2o9b
ob4obob2obob2o9bob2o2b2ob2obob2o9bo2b2ob2obo2bob2o9bob3ob2ob2obob2o$
72bobo2bo2bobob2o6bob2obo4b2obob2o8bobo9bob2o9bo7bo3bob2o9bobo6bo2bob
2o9bo11bob2o9bo11bob2o9bo11bob2o9bo11bob2o9bo11bob2o$35b2o16b2o2b2o14b
9o10bo8bo3bob2o9b11o14b11o14b11o14b11o14b11o14b11o14b11o14b11o$35b2o
16b2o2b2o34b12o$75b2ob2o38b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob
2o16b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o$75b2ob2o13b2o2b2o2b
2o15b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o16b2o2b
2ob2o16b2o2b2ob2o16b2o2b2ob2o$93b2o2b2o2b2o4$4b2o4b2o$5bo5bo$4bo5bo24b
2o16b2o15b2ob2o$4b2o4b2o23b2o16b2o15b2ob2o$6bob2o$6b2obo23b4o14b4o13b
9o$10b2o17b2obo2bobo9b2obo2bobo11bo9bo$11bo17b2obobo2bo9b2obobo2bo11b
2o2b3o2b2o$10bo21bobo2bob2o9bo3b2ob2o5b2obo9bob2o$10b2o20bo4bob2o9bo4b
ob2o5b2obo3bobo3bob2o$33b4o14b4o12b2o3bo3b2o$10b2o55bo2bo3bo2bo$10b2o
23b2o16b2o13b9o$35b2o16b2o$70b2ob2o$70b2ob2o7$35b2ob2ob2o$35b2ob2ob2o$
7b2obo$7bob2o22b12o$5b2o25bo12bo$5bo26bobobo3bob2obo$6bo22b2obob2o3b2o
bo2bob2o$5b2o22b2obo12bob2o$7b2obo21bob2o3b2obo2bo$7bob2o18b2obobobo3b
ob2obob2o$5b2o4b2o16b2obo12bob2o$5bo5bo21b12o$6bo5bo$5b2o4b2o22b2ob2ob
2o$7b2obo24b2ob2ob2o$7bob2o9$7bob2o$7b2obo24b2o18b2o2b2o14b2o2b2o14b2o
2b2o14b2o2b2o14b2o2b2o19b2o2b2o19b2o2b2o19b2o2b2o19b2o2b2ob2o16b2o2b2o
b2o16b2o2b2ob2o$11b2o22b2o18b2o2b2o14b2o2b2o14b2o2b2o14b2o2b2o14b2o2b
2o19b2o2b2o19b2o2b2o19b2o2b2o19b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o$12bo
$11bo21b6o14b8o12b8o12b8o12b10o10b10o15b10o15b10o15b10o15b11o14b11o14b
11o$11b2o19bobo4bo12bo8bo10bo8bo7b2obo8bo10bo10bo8bo10bo13bo10bo13bo
10bo13bo10bo10b2obo11bo9b2obo11bo9b2obo11bo$9b2o21bo3b2obo12bo3b3o2bo
10bo3b4obo7b2obo3b3o2bo10bo3b4o3bo8bo3b4o3bo13bo3b4o3bo13bo3b4o3bo13bo
3bo2bo3bo10b2obobob7obo9b2obo3b2ob3o2bo9b2obo3b2ob3o2bo$10bo18b2ob2o3b
obob2o6b2obobobo2bobob2o4b2obobobo2bobob2o7bobo2bo3bob2o4b2obobobo2bob
obob2o2b2obobobo2bobobob2o7b2obobobo2bobobob2o7b2obobobo2bobobob2o7b2o
bobob4obobob2o10bobobo2bo4bob2o9bobobob2o4bob2o9bobo2b2obo3bob2o$9bo
19b2obo2bo3bob2o6b2obobo4bobob2o4b2obobo4bobob2o7bob2o3bobob2o4b2obobo
6bobob2o2b2obobo6bobob2o7b2obobo6bobob2o7b2obobo6bobob2o7b2obobo6bobob
2o10bobo6b2obob2o9bobo6b2obob2o9bob2o6bobob2o$9b2o21bob3o2bo12bob6obo
10bob6obo7b2obobo3b2obo10bob2o4b2obo8bob2o4b2obo13bob2o4b2obo13bob2o4b
2obo13bob8obo10b2obob2o6bobo9b2obob2o6bobo9b2obobo6b2obo$7b2o23bo6bo
12bo8bo10bo8bo7b2obo3bo2bobo7b2obo3bo2bo3bob2o2b2obobo6bobob2o7b2obo
10bob2o7b2obo3bo2bo3bob2o7b2obo10bob2o7b2obobo7bobo9b2obo2bo5bo2bo9b2o
bo2bo5bo2bo$8bo24b6o14b8o12b8o11bo2b3o3bob2o4b2obo3bo2bo3bob2o2b2obobo
bo2bobobob2o7b2obob2o4b2obob2o7b2obob2o4b2obob2o7b2obob8obob2o10bobo6b
2obob2o9bobo6b2obob2o9bob2o6bobob2o$7bo84bo8bob2o7bob2o4b2obo8bo3b4o3b
o13bobo6bobo13bobo6bobo13bobo6bobo10b2obob2o6bobob2o6b2obob2o6bobob2o
6b2obobo6b2obob2o$7b2o26b2o18b2o2b2o14b2o2b2o12b8o8b2obobo6bobob2o5bo
10bo13bobobo2bobobo13bobobo2bobobo13bobob4obobo10b2obo4bo2bobobo9b2obo
4b2obobobo9b2obo3bob2o2bobo$35b2o18b2o2b2o14b2o2b2o28b2obobobo2bobobob
2o6b10o11b2obo3b4o3bob2o7b2obo3b4o3bob2o7b2obo3bo2bo3bob2o10bob7obobob
2o9bo2b3ob2o3bob2o9bo2b3ob2o3bob2o$93b2o2b2o13bo3b4o3bo30b2obo10bob2o
7b2obo10bob2o7b2obo10bob2o10bo11bob2o9bo11bob2o9bo11bob2o$93b2o2b2o13b
o10bo11b2o2b2o17b10o15b10o15b10o15b11o14b11o14b11o$113b10o12b2o2b2o$
160b2o2b2o19b2o2b2o19b2o2b2o17b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o$115b
2o2b2o39b2o2b2o19b2o2b2o19b2o2b2o17b2o2b2ob2o16b2o2b2ob2o16b2o2b2ob2o$
115b2o2b2o5$7b2obo$2o5bob2o143b2obo21b2o2b2o2b2o2b2o$o10b2o22b2ob2o2b
2ob2o24b2o3b2o4b2o70bob2o4b2o15b2o2b2o2b2o2b2o38b2obo6b2obo$bo9bo23b2o
b2o2b2ob2o24bo5bo5bo22b2o2b2ob2o43b2o2bo68bob2o6bob2o20b2o2b2o2b2o2b2o
$2o10bo59bo3bo5bo23b2o2b2ob2o43bo4bo13b18o40b2o2b2o4b2o18b2o2b2o2b2o2b
2o$o10b2o20b16o22b2o3b2o4b2o75bo2b2o12bo6bo11bo39bo3bo5bo$bo5b2obo21bo
12bo3bo21bo6bob2o22b13o41b2o2bo13bo2b3o3b2ob5ob2o40bo3bo5bo16b18o$2o5b
ob2o21b2o2b3o2b2o5b2o22bo5b2obo21bo13bo36b2obo5bo9b2obobo7bobo2bo3bob
2o36b2o2b2o4b2o15bo2bo3bo11bo$o4b2o22b2obo9bo6bob2o18b2o9b2o19bo3b4ob
4obo36bob2o4b2o9b2obobo7bobo4bobob2o32b2obo6b2obo17b2o3bo3b2ob5ob2o$bo
3bo23b2obo3bobo3bob2o3bob2o18bo11bo16b2obobobo2bobo2bobob2o31b2o8bo13b
o2b3o3b2ob6obo35bob2o6bob2o14b2obo3bobo3bobo2bo3bob2o$2o4bo25b2o3bo3b
2obo3b2o22bo9bo17b2obobo4bobo4bob2o31bo10bo12bo6bo11bo33b2o8b2o4b2o12b
2obo9bobo4bobob2o$o4b2o25bo2bo3bo9bo21b2o9b2o19bob6ob2o3bo35bo8b2o13b
18o34bo9bo5bo16b2o2b3o2b2ob6obo$bo5b2obo22b16o22bo31bo13bo34b2o8bo67bo
9bo5bo15bo18bo$2o5bob2o61bo9b2o20b13o37b2obo5bo15b2o2b2o2b2o2b2o36b2o
8b2o4b2o16b18o$35b2ob2o2b2ob2o24b2o9b2o70bob2o4b2o15b2o2b2o2b2o2b2o38b
2obo6b2obo$35b2ob2o2b2ob2o59b2o2b2ob2o116bob2o6bob2o20b2o2b2o2b2o2b2o$
106b2o2b2ob2o150b2o2b2o2b2o2b2o!

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Re: Thread For Your Useless Discoveries

Postby towerator » September 6th, 2014, 12:55 pm

Bob: those are billard-table oscillators. This term means that the stator entirely contains the rotor (the stator can be somewhat "open" in some cases). Furthermore, most of your oscillators are either clones with the same rotor, either already known, I fear.
finally, the 3 last ones are "trivial oscillators". It means that no cell has a period of 14/21/28, and that therefore we have to consider it as two separates oscillators.
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Re: Thread For Your Useless Discoveries

Postby A for awesome » September 14th, 2014, 1:37 pm

Interesting, but useless, predecessor of a p2 oscillator:
x = 10, y = 10, rule = B3/S23
4b2o$3bo2bo$3bobo$b2obo3bo$o2b2o2bobo$obo2b2o2bo$bo3bob2o$4bobo$3bo2bo
$4b2o!

Note how the bakery is destroyed and later reforms.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread For Your Useless Discoveries

Postby A for awesome » September 16th, 2014, 5:19 pm

Schick-based puffer emits a LWSS each period.
x = 410, y = 54, rule = B3/S23
348bo$347bo47bo$348bo45bobo$355b2o37bo2bo$354bo2b2obo34b2o$319bo34bo4b
obo9bo$317bobo36b2o3bo9bo$316b2o28b2o7bo3bobo7bo8bo$315b2o4bo25bobo3b
2o5bo3b2o3b2o6bo2bo$317bob3o25b2obo2bo2bo2bobo2b2ob2obobo3bo4bo$319b2o
28bo3b2obobo2b2ob6obo3bo5bo$312bo36b2o10bo6bo11b2o$312b4o37bo5bo16bo2b
o$311bo2bo2bo59b3o$312b4o8bo$64bo82bo47bo47bo47bo20bo10b3o13bo$64bo26b
2o4b2o9bo30b2o5bobo38b2o5bobo38b2o5bobo46bo25bo5b3o13bo$64bo26b2o3b2ob
2o6bobo29b2o5b2o39b2o5b2o39b2o5b2o47bo25b3o3b2ob2o9bo$107bobo212bo3b2o
8b3o30bo10b3o$98bo9bo161b3o50b2o10bo33bo$89bo4b2o2bo2bo2b2o163b5o6b2o
44b2o7bo2bo29bo$87bobo5bo2bo4bob2o5b2o39bo6b2o39bo6b2o11b2o26bo6b2o10b
2o3b2o5b3o21b2o9b2o6b5o7b2ob2o12b2o14b3o16bo12b2o$86b2o5bo2bo4b3o8b2o
38bobo5b2o38bobo5b2o10bo2bo24bobo5b2o9b3o3bo9bo20b2o8bo2bo5b5o9b2o13b
2o14b2ob2o14bo12b2o$94b2o2bobo3bo48b2o15b2o29b2o18b2o26b2o17b5o8bo32bo
2bo51bo2bo14bo$93b3o12bo31b2o28b2o16b2o46b2o31bob2o7bobob2o28b2obo12bo
bo36bo2bo$93bobo12bo31b2o46b2o46b2o32bo9bo4bo28b2ob2o13b2o35bobo11b3o
3b3o$56b2o10bo24bobo184b5o30bo2bo13b3o32b2ob2o$55bo11bobo24b2o24b2o
160b2o32b2o14b2o5b2o26b2ob2o15bo$39bo15b3o2b3o4bobo49bo2bo114bo86b3o5b
ob4o2b2o19bo7bo17bo$38b3o20b2o5bo50bo2bo2b2o45bo58b4obobo59b2o24b2o6bo
bob2o8b2o12bo26bo$37b2o2bo15b2ob3o56bo4bo2bo43b3o56b7ob2o58b2o34bo4bo
6b2o$38bo2bo15b4o17bo41bobo6b2o40b4o47b2o5b2obo3bo97b2o2b2o20bo2bo$38b
o2bo15bo3bo15bobo43bo7bo42b2o43b2o2bo4b3ob2obobo45b2o49b2o2b2o45bo$58b
o2bo16bo42bo5bo2bo43b2o56bo2bo46bo2bo51bo47bo$15b3o25bo15b3o59bo6b2o
44bo43bo3bo12bo32b3o11bobo48bob3o47bo$14b5o20b2o128b2o2b2o43bo3b3ob3o
44b2o8bo50b3o$13b2ob3o45b2o153b2o2b4obo3bob2o37b2o106b3o$14b2o20b2o3b
2o19b2o2bo106bo49bo3b2o4b2o85bo15b3o$24bo12bo2b3o18b2ob2o81b2o24bo21b
2o26bobo7bo9b2o34b2o10b2o26bobo$23bobo13bob2o104b2o24bo21b2o38bo7b2o
34bobo9b2o25bobo6b2o36b2o$b2o19bo3bo12b3ob2o72b2o46b2o68bo44bo37b2o45b
2o$2ob2o8bo9bobo17b2o72b2o46b2o51b2o99b3o$b4o3bo4bobo23b2o2b2o16b2obob
o11bo138bo2bo99bobo9b3o$2b2o3bo5bo2bo6bo15bob2o6b2o14b3o11bo64b2o46b2o
24b2o20b2o22b2o22b2o22b2o5b2obo8bo2bo25b2o46b2o$6bo2bo6bo7b2o14b2o6bo
2bo15bo11bo35b2o27bobo16b2o27bobo16b2o27bobo16b2o3b2o10b3o9bobo16b2o3b
2o7bo8bo2b2o20b2o3b2o41b2o3b2o$2b2o3bo5bo2bo5bobo15b2o7b2o14b3o47b2o
28bo17b2o28bo17b2o28bo17b2o28bo17b2o22b2o22b2o46b2o$b4o3bo4bobo7bo118b
o47bo47bo35bo5bo5bo40bo3bo$2ob2o8bo79b3o46bo47bo47bo35bo5bo5bo39bo$b2o
139bo47bo47bo35bo5bo5bo43b2o$69bo47bo47bo47bo47bo47bo21b2o24bo47bo$69b
o47bo47bo47bo47bo14b3o30bo20b2o25bo47bo$69bo47bo47bo47bo47bo47bo16bob
3o26bo47bo$327b2o46b3o$328bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread For Your Useless Discoveries

Postby codeholic » September 16th, 2014, 5:25 pm

Did you get it from this post?
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Re: Thread For Your Useless Discoveries

Postby A for awesome » September 17th, 2014, 10:55 am

That's funny! I discovered this independently a few months ago, and now someone beats me to posting it by less than a week. Oh, well.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread For Your Useless Discoveries

Postby A for awesome » September 18th, 2014, 1:14 pm

P2 billiard table with 8 different interdependent rotors:
x = 17, y = 20, rule = B3/S23
10b2o$10bo$5b2o4bo$5bo4b2o$6b3o6b2o$9b5o2bo$4b3o7b2o$3bobob5o$3bobo4bo
b4o$4b3ob2o5bo$bo6b5o$b4o8bo$4b6o3bo$b3o5b4o$o2b6o$2o6b3o$5b2o4bo$5bo
4b2o$6bo$5b2o!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread For Your Useless Discoveries

Postby BobShemyakin » September 19th, 2014, 4:40 am

I found a few oscillators:
x = 166, y = 139, rule = B3/S23
120b2o2b2o$120b2o2b2o$76b2o2b2o2b2ob2o10b2o$7b2obo18bo12bo3bo12bobo4bo
9b2o2b2o2b2ob2o12bo16b10o$7bob2o16bobo10bobobobobo11bo2b2obobo29bo18bo
3bo6bo$11b2o13bo4bo10bobo13b2o3b3obo6b15o9bob4o13bob2obo3bobo$11bo15b
4obo6b2obob6o10b2o3bo2bo5bo13bo7bobo6bo8b2obo2b4ob2obob2o$12bo11b2obo
2bo11bo16b2o16b3ob2ob3o8bo2bo3bo2bo8b2obo7bob2ob2o$11b2o14bo2bob2o6b3o
3b3o10b2o5b2o8bo4b2o12bo6bobo12bo2bob2ob2obo$7b2obo14bob4o15bo19b2o13b
2o4bo9b4obo14bob2ob2obo2bo$7bob2o15bo4bo7b6obob2o8bo2bo3b2o10b3ob2ob3o
15bo11b2ob2obo7bob2o$5b2o21bobo13bobo12bob3o3b2o6bo13bo9bo14b2obob2ob
4o2bob2o$5bo22bo11bobobobobo9bobob2o2bo8b15o10b2o15bobo3bob2obo$6bo35b
o3bo13bo4bobo49bo6bo3bo$5b2o68b2ob2o2b2o2b2o30b10o$7b2obo64b2ob2o2b2o
2b2o$7bob2o109b2o2b2o$120b2o2b2o4$97b2ob2o$31b2o19bo44b2ob2o$30bo2bo
18b3o12bo11b2o$30b3o17b2o3bo9bobobo9bo2b2o13b2ob4ob2ob2o$49bobob3o9bob
obobo8bobobob2o9b2obo2bob2ob2o$30b3o16bobo4b2o6bobobobo8b2obob2obo13bo
bo$30bo2bo14b2o4bobo9bobobo7bo18b3o5b2ob2o$32bobob2ob2o9b3obobo11bo9b
3o3b3o10bo6bobob2o$30bo6bobobo8bo3b2o30bo7b2obobo6bo$25bo3bo5bobobobo
9b3o23bob2obob2o8b2ob2o5b3o$24bobobobo5bo3bo12bo23b2obobobo15bobo$24bo
bobo6bo45b2o2bo8b2ob2obo2bob2o$25b2ob2obobo50b2o8b2ob2ob4ob2o$32bo2bo$
33b3o66b2ob2o$102b2ob2o$33b3o$32bo2bo$33b2o7$50b2o28b2o24b2o$50b2o27bo
2bo22bo2bo18bo$3b2obo72b3o23b3o17b3o$3bob2o20b2o4b2o15b4ob2o19bo7bo17b
o7bo13bo$7b2o15bo2bo6bo2bo9bobo3bobo20b9o17b9o12bobob3o3b2o$7bo15bobob
obo2bobobobo8b2obo5bo13b2o51bobobo2bobobo$8bo15bo2bobo2bobo2bo12bob4ob
ob2o10bo2b6ob2o19b2obobob2o11b2obo4bobo$7b2o18bobo2bobo12b2obo6bob2o
10bobo5bo3bo14b2obo2bobobo2bob2o10bobo2bob2o$3b2obo21bo4bo13bo2bo3bo2b
o10b2obobob2o4bobo15bobo2bo3bo2bobo11bobo4bo$3bob2o37b2obo6bob2o9bobob
o4bo3b2obob2o9bo2bo2b2o2bo2b2o2bo10b2obo2bobo$7b2o35b2obob4obo12bobobo
b2o8bobo9bobobobo4bo4bobob2o8bo2b3ob2o$7bo40bo5bob2o10bo2bobo9bobo9bob
obo2bob2ob2obo2bobobo7bo$8bo40bobo3bobo13bobo8b2obob2o7b2obobo4bo4bobo
bobo8b3o$7b2o39b2ob4o15b2obob2o3bo4bobobo9bo2b2o2bo2b2o2bo2bo11bo$3b2o
bo66bobo4b2obobobobo9bobo2bo3bo2bobo$3bob2o46b2o18bo3bo5bobo2bo9b2obo
2bobobo2bob2o$53b2o19b2ob6o2bo16b2obobob2o$85b2o$72b9o21b9o$72bo7bo21b
o7bo$75b3o27b3o$75bo2bo25bo2bo$76b2o27b2o6$51b2o20bo19b2o$49bo2bo19bob
o18b2o$2o4b2o19b2ob2o17b3o21bo$bo5bo19b2ob2o59b4o17b2o2b2o14b2o2b2o14b
2o6b2o$o5bo40b7o17b5o14bo4bo15bobo2bobo12bobo2bobo9b2obobo6bobo$2o4b2o
17b7o14bo3bo3bo15bo5bo13bob2obo15bo6bo12bo6bo9b2obo4b2o4bo$2bob2o15b2o
bo7bob2o7bo2bobo3bobo2bo12bo2b2obo10b2obo2bobob2o9b2ob2o5bob2o6b2ob2o
5bob2o9b2o2bo2bo2b2ob2o$2b2obo14bobob3o3b3obobo5bobobo2bobo2bobobo8b2o
bobobobob2o7b2ob2obobob2o9b2obo2bobobob2o6b2obo2bobobob2o9bobo2b2o2bob
ob2o$6b2o12bobobo2bobo2bobobo6bo2b2obobob2o2bo9b2obobo3bob2o10bo4bo15b
obo2bobo12bobo2bobo9b2obo2b2o2b2o2bo$7bo13bo3b2o3b2o3bo10bo7bo15bobo3b
o13bo4bo15bobo2bobo9b2obo2bobobob2o6b2obo4b2o4bo$6bo40b7o13b2obobo3bob
2o7b2obobob2ob2o9b2obobobo2bob2o6b2ob2o5bob2o9bo2b2o2b2o2bob2o$6b2o59b
2obobobobob2o7b2obobo2bob2o9b2obo5b2ob2o9bo6bo9b2obobo2b2o2bobob2o$49b
3o18bo2b2obo13bob2obo15bo6bo12bobo2bobo9b2ob2o2bo2bo2b2o$48bo2bo18bo5b
o13bo4bo15bobo2bobo13b2o2b2o13bo4b2o4bob2o$6b2o40b2o21b5o15b4o17b2o2b
2o33bobo6bobob2o$6b2o144b2o6b2o$73bo17b2o$72bobo16b2o$73bo7$2b2obo22bo
2bo$2bob2o22b4o$2o$o22b2ob8ob2o$bo22bobo6bobo$2o19bo2bobob4obobo$2b2ob
o14bobobo3bo2bo3bob2o$2bob2o14bobobo10bobobo$6b2o13b2obo3bo2bo3bobobo$
6bo17bobob4obobo2bo$7bo16bobo6bobo$6b2o15b2ob8ob2o$2b2obo$2bob2o22b4o$
28bo2bo12$3b2obo21b2o2b2o$3bob2o22bo2bo4bo$b2o4b2o15b2obo6bobobo$bo5bo
15bobob2o4b2obobo$2bo5bo14bobo10bobob2o$b2o4b2o11b2obob2obo4bob2obob2o
$3b2obo13b2obobo10bobo$3bob2o16bobob2o4b2obobo$b2o4b2o14bobobo6bob2o$b
o5bo16bo4bo2bo$2bo5bo19b2o2b2o$b2o4b2o$3b2obo$3bob2o!

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Re: Thread For Your Useless Discoveries

Postby A for awesome » September 22nd, 2014, 1:15 pm

7-cell, 3x5 methuselah lasts 1675 gens.
x = 5, y = 3, rule = B3/S23
2b2o$bobo$2o2bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread For Your Useless Discoveries

Postby Lewis » September 27th, 2014, 4:28 pm

Two blocks + four stairstep hexominoes -> P6 A for All (+ loads of other stuff):
x = 16, y = 16, rule = B3/S23
3bo8bo$3b2o6b2o$4b2o4b2o$5bo4bo4$2o12b2o$2o12b2o4$5bo4bo$4b2o4b2o$3b2o
6b2o$3bo8bo!


EDIT: two fleet predecessors + pond -> some p5 fumarole-thing...
x = 8, y = 20, rule = B3/S23
2o$obo$b2o$3bo5$5b2o$4bo2bo$4bo2bo$5b2o5$3bo$b2o$obo$2o!
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Re: Thread For Your Useless Discoveries

Postby Lewis » September 28th, 2014, 4:53 am

4 blocks + some junk -> twin bees shuttle variant (amongst other things):
x = 27, y = 21, rule = B3/S23
11b2ob2o$11b2ob2o2$3o21b3o$2ob3o15b3ob2o12$2ob3o15b3ob2o$3o21b3o2$11b
2ob2o$11b2ob2o!

APGsearch doesn't properly detect this, it just labels it as 'OVERSIZED'.
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Re: Thread For Your Useless Discoveries

Postby Extrementhusiast » September 28th, 2014, 2:39 pm

Lewis wrote:4 blocks + some junk -> twin bees shuttle variant (amongst other things):
x = 27, y = 21, rule = B3/S23
11b2ob2o$11b2ob2o2$3o21b3o$2ob3o15b3ob2o12$2ob3o15b3ob2o$3o21b3o2$11b
2ob2o$11b2ob2o!

APGsearch doesn't properly detect this, it just labels it as 'OVERSIZED'.


That "some junk" is the same as four R-loaves, just along a slightly different predecessor path:
x = 23, y = 21, rule = B3/S23
9b2ob2o$9b2ob2o$2o19b2o$obo17bobo$o2bo15bo2bo$b2o17b2o10$b2o17b2o$o2bo
15bo2bo$obo17bobo$2o19b2o$9b2ob2o$9b2ob2o!
I Like My Heisenburps! (and others)
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Re: Thread For Your Useless Discoveries

Postby Scorbie » September 29th, 2014, 2:42 am

This is from "Thread For Your Accidental Discoveries" thread.
codeholic wrote:
Alexey_Nigin wrote:Five 2c/5 spaceships can pull a bi-block.

Ha! Nice base for a rubegoldbergian sawtooth! :)

Ha! I think I made that rubegoldbergian sawtooth!
(Warning: It's veeery slow and painful to watch. Hyperspeed recommended.)
x = 1075, y = 854, rule = B3/S23
21b2o$21b2o5$21b3o820b2o$21b3o818bo2bo$20bo3bo$841bo$19b2o3b2o$842b2o$
844bo3$29b2o2b2o4bo2b2o12b2o783b2o3b2o$29b2ob2o6b2obo12b2o783b2o3b2o$
33bobo6bo799b5o$14bo19b2o4b3o43b2o755bobo$12b4o70b2o722bo2bo$6b2o3bobo
b2o17b2o4b3o770bo7b3o19b3o$6b2o2bo2bob3o15bobo6bo766bo9bo4bo11b2o$11bo
bob2o15b2o6b2obo12b2o751b2o8bo5bo10b2o$12b4o17b2o4bo2b2o12b2o28bo728bo
8bo$14bo70bobo724b2o8b2o25bo$84bo3bo758bobo$85b3o724b2o8b2o21b2o12b2o$
83b2o3b2o725bo8bo20b2o12b2o$15b2o5b2o42bo742b2o8bo5bo19b2o$13bo2bo5bo
2bo23b2o15b2o8b2o731bo9bo4bo22bobo$49b2o16b2o7b2o735bo7b3o25bo$18bobo
41b2o2b2o27bobo712bo2bo$13b2o3bobo3b2o64bo4bo2bo$53bo37b2o5b2o6b2o10b
2o729b2o$17bo3bo29b5o30bo9bo3b2o4b2o10b2o729b2o$50bo2bob2o5b2o2b2o18bo
11b2o$49bo7bo9b2o7b2o17bo2bo$50bo2bob2o9b2o8b2o17bobo663b2o$15b2o5b2o
27b5o10bo694b2o$53bo$14bo9bo$14bo3bobo3bo66b2o24b3o$14bo3bobo3bo66b2o
23bo3bo$15bobo3bobo$16bo5bo92bo5bo724b2o3b2o$115b2o3b2o$84b3o3b3o33b2o
719bo3bo8b2o$83bo2bo3bo2bo30bo3bo630b2obob2o82b3o8b3o$87bobo28bo4bo5bo
8b2o708b3o5bob2o9b2o$83b2o7b2o23bobo2b2obo3bo8b2o619bo5bo90bo2bo4bo5bo
$83b2o7b2o23bobo3bo5bo620b2o104bob2o5bo$86bo3bo27bo5bo3bo621b2o8b2ob2o
94b3o3bo3bo$86b2ob2o35b2o613b2o3bo6b2o7bo97b2o5bo$84b3o3b3o648bobo3bo
5b3o$84b2o5b2o649b5o6b2o$15b2o67bo7bo650b3o4b2o$15b2o106b2o625b2o102b
2o$116b3o4b2o672b2o55b2o$797bo$115bo3bo667bo7bobo$10bobo102bo3bo617b2o
17b2o5bo20b4o7b2o$9bo2bo103bobo618b2o17b2o4b3o11b2o5b4o60b3o3b3o$8b2o
11bo26bo67b3o642b2ob2o10b2o5bo2bo59bo2bo3bo2bo$2o4b2o3bo9bo26b3o732b4o
63bobo$2o6b2o5b2o34bo708bobobobo17b4o58b2o7b2o$9bo2bo4bo32b2o735bo58b
2o7b2o$10bobo748b2ob2o83bo3bo$761b2ob2o83b2ob2o$84b2o5b2o23bo7bo638bo
83b3o3b3o$84b2o5b2o21bob2o5b2obo720b2o5b2o$18b2o3b2o89bo3b2ob2o3bo608b
2obob2o105bo7bo$20b3o92bo3bobo3bo708b2o5b2o$19bo3bo26b2o3b2o59b3o3b3o
610bo5bo91bobo5bobo$20bobo30bo672b2o104b3o7b3o$21bo28bo5bo669b2o8b2ob
2o91b2ob3ob3ob2o$51b2ob2o661b2o3bo6b2o7bo94b5ob5o$52bobo88b2o572bobo3b
o5b3o103bo5bo$53bo89b2o573b5o6b2o24b2obo3bob2o70b2ob2o$20b2o31bo665b3o
4b2o27bo2bo3bo2bo$20b2o704b2o28b3o3b3o2$835bo5bo$834b2o5b2o$52b2o62b2o
5b2o17b3o587b2o99bob2o3b2obo3b2o5b2o$52b2o62b2o5b2o607b2o99bob2o3b2obo
3b2o5b2o$142bobo689b3o3b3o$141b5o688b3o3b3o$140b2o3b2o609b2o5b2o$140b
2o3b2o609b2o5b2o$152b2o$152bobo$143bo3b2o6bo7b2o$142bobobo2bo2bo2bo7b
2o$142bobo2b2o6bo$143bo8bobo$152b2o547b2o30bo5bo$701b2o29b3o3b3o$731b
2ob2ob2ob2o$730b3o7b3o98b2o$148b2o691b2o$148b2o582bo7bo2$701b3o$700b2o
b2o142b2o$79b2o61bo5bo551b2ob2o101b2o39b2o4b3o$79b2o60b3o3b3o550b5o
101b2o36b2o6b5o$140b2o2bobo2b2o548b2o3b2o137b3o5bo3bobo$140b2ob2ob2ob
2o685bo7b2o6bo3b2o$143b2ob2o544b2o140b2ob2o8b2o$141bobo3bobo540bo2bo
153b2o$140bo2bo3bo2bo27b2o501b2o6bo7b6o29b2o5b2o92bo5bo$143bo3bo30b2o
501b2o6bo6bo6bo28b2o5b2o64b3o$140bobo5bobo538bo7b2o4bo100b2ob2o24b2obo
b2o$79b3o59bo7bo540bo2bo7b2o101b2ob2o$78bo3bo609b2o110b5o$77bo5bo719b
2o3b2o$77b2obob2o$72bo742b2o$71bobo622b2o117bo2bo$59b2o9bo3b2o4bo615b
2o108b6o7bo6b2o$59b2o9bo3b2o3bobo93b2obob2o623bo6bo6bo6b2o$70bo3b2o3bo
bo723bo4b2o7bo16b2o$71bobo6bo94bo5bo515bo5bo102b2o7bo2bo17b2o$72bo116b
2o505b3o3b3o110b2o$176b2ob2o8b2o505bob2ob2obo$178bo7b2o6bo3b2o495b2o7b
2o$141b2o5b2o35b3o5bo3bobo495b2o7b2o$74b2o22bo42b2o5b2o36b2o6b5o496b3o
5b3o80b2o17bo5b2o$72bo2bo14bo6bobo89b2o4b3o499b3ob3o80bo2bo7b2o7b3o4b
2o$80b3o6bobo3b2o3bo9b2o77b2o508bobo73b2o6bo7b2o4bo5b2ob2o$77bobo3bo5b
obo3b2o3bo9b2o555b2o27bo2bobo2bo70b2o6bo6bo6bo$72b2o3bobo3bo6bo4b2o3bo
566b2o26bo2bo3bo2bo77bo7b6o5bobobobo$81b2o14bobo596b2o5b2o79bo2bo$76bo
3bo17bo84b2o16b2o465bo117b2o15b2ob2o$87b2obob2o89b2o16b2o464bobo133b2o
b2o$87bo5bo16b2o555bobo123b2o3b2o5bo$88bo3bo17b2o556bo125b5o$74b2o5b2o
6b3o109bo592b2ob2o$200bobo516bo74b2ob2o$73bo9bo26b3o86bo3bo461b2obob2o
45b2o76b3o$73bo3bobo3bo26b3o37bo48b5o461bo5bo46b2o$73bo3bobo3bo60bo3bo
bo47b2o3b2o461bo3bo99b2o$74bobo3bobo62bo3b2o48b5o463b3o100b2o$75bo5bo
61b3o31bo5bo16b3o452bo70bobo41b2o$108b2o3b2o61b3o3b3o16bo452bobo69b2o
42bo32b2obo3bob2o$90b2o17b5o62bob2ob2obo462b2o3b2o3bo38b2o5b2o22bo41bo
bo23b2o6bo2bo3bo2bo$90b2o18b3o65b2ob2o29bo434b2o3b2o3bo38b2o5b2o64bobo
23b2o7b3o3b3o$111bo66b2ob2o29bobo437b2o3bo112bo$98bo79b2ob2o32b2o4b2o
431bobo$97bobo115b2o4b2o432bo$90b2o4bob2o115b2o550b2o3b2o$90b2o3b2ob2o
112bobo552bobobobo$96bob2o112bo555b5o$97bobo562b2o105b3o$74b2o5b2o15bo
563b2o106bo12bo20b2o5b2o$74b2o5b2o62bo585bo50b4o18b2o5b2o$146bo59b2o
523bobo47b2obobo3b2o$144b3o59b2o523b2o47b3obo2bo2b2o$105b2o27bo604bobo
39b2obobo$105b2o4b3o19bobo603b2o41b4o$133b2obo4b2o33b2o5b2o555bo42bo$
110bo3bo18b2ob2o3b2o28bo4b2o5b2o$110bo3bo18b2obo32bobo$111bobo19bobo
34b2o58b2o$111b3o20bo95b2o515bo27b2o$121bo623b4o26b2o$120b3o540bo5bo
69b2o3bobob2o$119b5o47bo490b3o3b3o68b2o2bo2bob3o$118b2o3b2o13b2o29bobo
58bo430bo3bobo3bo72bobob2o$138bobo29b2o57b3o429bo9bo73b4o$105bo7bo25b
3o57b3o3b3o20bo3bo429b3o3b3o20bo55bo12bo$103bob2o5b2obo24b2o57bo2bobo
2bo19bob3obo393b2o61bo68b3o$103bo3b2ob2o3bo4b3o17b2o35bo21b2obobob2o
20b5o394b2o61b3o45b2o18b5o6bo5bo$104bo3bobo3bo5b3o15bobo35bo22b2o5b2o
530b2o17bobobobo4b3o3b3o$105b3o3b3o25bo36b3o578b2o3b2o3bo2b2ob2o2bo$
166bo497b2ob2o98b3o5b3o$121b2o44bo72bo424bobo$121b2o13b2o3b2o22b3o67bo
4b4o417b2ob2ob2ob2o88bo$136b2o3b2o58b2ob2o29bo5b4o5b2o409bo2bo3bo2bo
87bobo$199bo2bobo2bo21bo11bo2bo5b2o409bo9bo87bobo$138b3o58bobo3bobo20b
o12b4o416bo2bo3bo2bo88bo$127bo10b3o58b3o3b3o20b3o9b4o384bo33b2o5b2o88b
2o$127b2o10bo34b3o22b2o5b2o32bo386b3o107b3o19b2o$118b2o2b2o4b2o43bo2bo
22b2o5b2o418b5o105bo3bo18b2o$118b2o2b2o4b3o45bo22b2o5b2o410bo6b2o3b2o
103bo5bo$105b2o5b2o8b2o4b2o46bo441bobo5b5o104bo5bo5bo$105b2o5b2o13b2o
44bobo59b2o370b2o12b2o3bo3bo51bo55bo6bobo$127bo107b2o370b2o12b2o4bobo
51bo54bo3bo3bobo11b2o$621b2o5bo52b3o53b3o3bo2bo11b2o$618bobo117bo5bobo
$618bo126bobo$133b2o26bo585bo20b2o5b2o$133b2o25b2o575bo30b2o5b2o$159b
2o4b2o2b2o566bo$158b3o4b2o2b2o451b2o59bobo$134bo5bo18b2o4b2o455b2o5bo
53b2o34bo23b2o$133b3o3b3o7bo10b2o466b3o53bo34bobo12b2o3b2o2b2o$133bob
2ob2obo6b3o10bo465bo3bo75b2o11bobo5bo$132b2o7b2o5b3o476b2ob2o75b2o11bo
2bo3b3o$132b2o7b2o577bobo3bo3bo$132b3o5b3o3b2o3b2o13b2o60b3o3b3o391b3o
88bobo6bo$134b3ob3o5b2o3b2o13b2o60bo2bobo2bo391b3o88bo5bo5bo$136bobo
89b2obobob2o488bo5bo2b2o3b2o$133bo2bobo2bo86b2o5b2o470b2o17bo3bo$132bo
2bo3bo2bo6bo557b2o18b3o$133b2o5b2o6bobo586bo$147b2o588bo$147b2o475b2ob
2o18bobo$147b3o80b2ob2o389b2ob2o19b2o$148bobo77bo2bobo2bo387b2ob2o19bo
59bo27bo7bo$149b2o77bobo3bobo385bob2ob2obo77bo27b2o5b2o$166b3o59b3o3b
3o385b3o3b3o76bobo26b3o3b3o$165bo3bo58b2o5b2o17b2o5b2o360bo5bo76b2ob2o
27b2ob2o$156bobo5bo5bo57b2o5b2o17b2o5b2o442bo5bo15b2o9bo3bo$156bo3bo4b
o3bo58b2o5b2o471bo18b2o6b2o7b2o$146b2o12bo5b3o536b2o3b2o23b2o7b2o$146b
2o8bo4bo4b3o548b2o20bobo$160bo556bobo15bo2bo3bo2bo$133b2o5b2o14bo3bo
547bo3b2o4b3o7b2o6b3o3b3o$133b2o5b2o14bobo548bob3o2bo4b3o6b2o$707bob2o
b2o4b3o$622b2o5b2o77bo8bobo$622b2o5b2o86b2o17b2o5b2o$161b2o23bobo547b
2o5b2o$161b2o21bo3bo$184bo12b2o507b3o$176b3o4bo4bo8b2o489b2o16b3o4b2o$
176b3o5bo502bobo8bo6bo3bo3b2o$175bo3bo4bo3bo488b2o7b3o4b2ob2obo4bo5bo$
174bo5bo5bobo64b3o5b3o413b2o6b3o4bo2b3obo5b2ob2o$162bo5bo6bo3bo73bo2b
2ob2o2bo422b3o4b2o3bo$161b3o3b3o6b3o75b3o3b3o302b2o120bobo15b2ob2o$
160b2o2bobo2b2o84bo5bo48b2o252bo2bo120b2o14bo5bo$160bo3bobo3bo23b2o
114b2o255bo127b2o3b2o3bo3bo$160bob2o3b2obo23b2o371bo108b2o20bo7b3o$
160b2o7b2o394bobo108b2o17bo5bo4b3o$565bobo128b2ob2o$310bo255bo130bobo$
267b3o39b3o386bo$265b2obob2o8b3o8b2o15bo3bo363bo21bo$265b2o5bo5bo3bo8b
2o14bob3obo249b2o3b2o105bobo$177b2o86b2obob2o5bo4bo25b5o250bo5bo104bo
3bo$177b2o88b3o7bo3bo393b3o27b2o7b2o$564bo3bo104b2o3b2o25bob2o3b2obo$
277bo3bo271b2o10b3o129b2o6bo3bobo3bo$192b2o3b2o78bo4bo37bo137b2o91bo3b
o141b2o6b2o2bobo2b2o$183bobo8b3o67b2o12bo3bo8b2o22bo4b4o134b2o85b2o3bo
5bo149b3o3b3o$183bo2bo6bo3bo66b2o14b3o8b2o22bo5b4o5b2o213b2o2b2obo3bo
128bobo19bo5bo$174b2o10b2o6bobo124bo2bo5b2o218bo5bo123bo4bo2bo$174b2o
8bo3b2o5bo125b4o226bo3bo125b2o5b2o6b2o$161b2o5b2o9b2o5b2o132b4o229b2o
121bo9bo3b2o4b2o$161b2o5b2o8bo4bo2bo133bo137bo215b2o12b2o$183bobo87b2o
181b2ob2o214b2o8bo2bo$200bo73bo410bobo18b2o5b2o$198bobo73bobo10bo167bo
5bo82b2o14b2o144b2o5b2o$199b2o74b2o9b4o25b2o227b2o13bobo$189b2o24bobo
67b2obobo3b2o19b2o16b2o120b2obob2o96b3o6bo$189b2o23bo2bo66b3obo2bo2b2o
36bobo210bo12b2ob3ob2ob2o85bobo23b2o$213b2o10b2o58b2obobo40b3o104bo
105bobo12b5ob2ob2o84bo2bo23b2o$205bo5b2o3bo8b2o59b4o41b2o104b2o105bobo
14bo5bo77b2o6b2o11bo$204bobo6b2o5b2o65bo43b2o90b2o11b3obo9b2o93bo16b2o
b2o78b2o4b2o3bo9bo$203bo3bo6bo2bo4bo109bobo88b2o10b2o13b2o201b2o5b2o$
204b3o8bobo115bo102b2o216bo2bo4bo$190bo5bo5b2o3b2o228bo28bo75b2obob2o
106bobo$189b3o3b3o267bobo74bo5bo12bo5bo$188b2o2bobo2b2o131b2o3b2o100bo
10bo15bo3b2o3b2o68bo3bo12b2o5b2o$188bo3bobo3bo131b2o3b2o99b2o8b2obo14b
o3b2o3b2o69b3o12bob2o3b2obo$188bob2o3b2obo224b2o10b2o8b2ob3o13bo3b2o
62bo26bob2o3b2obo93b2o3b2o$188b2o7b2o109b3o3b3o15b3o88b2o11b3obo5bo2bo
15bobo63bobo26b3o3b3o96b3o$308b3o3b3o15b3o10bo91b2o8b2o17bo57b2o3b2o3b
o25b3o3b3o95bo3bo$307bob2o3b2obo15bo10b2o92bo85b2o3b2o3bo130bobo$307bo
b2o3b2obo25b2o4b2o2b2o174b2o3bo131bo7b2o5b2o$308b2o5b2o25b3o4b2o2b2o
176bobo140bob2ob2obo$309bo5bo27b2o4b2o181bo142bobobobo$205b2o137b2o
329bobobobo$205b2o138bo319b2o7bo7bo$429bo2bob2obo2bo224b2o$310b2ob2o
113b2o2bo4bo2b2o13bo83b2o$309bo5bo113bo2bob2obo2bo7bo4b3o83b2o$307b5ob
5o20b2o108b3obo109b2ob2o109b2ob2o$306b2ob3ob3ob2o12b3o4b2o107bob3obo
109bobo108bo2bobo2bo$306b3o7b3o133bo110bobo108b3o3b3o$307bobo5bobo12bo
3bo229bo110bo5bo$189b2o5b2o110b2o5b2o13bo3bo$189b2o5b2o133bobo116b2o
222b2o5b2o$331b3o116b2o222b2o5b2o2$511b2o26b3o3b3o$366b2o143b2o26bo2bo
bo2bo$366b2o171bo7bo$436b2o$331bo7bo97b2o101bo5bo$235bo21b2o70bob2o5b
2obo64b2o5b2o21bo104b2ob2o$197b3o32b4o20bobo15b2o53bo3b2ob2o3bo64b2o5b
2o$199bo31b4o5b2o13b2obo15b2o54bo3bobo3bo24b3o$198bo25b2o5bo2bo4bo2bo
13b2o73b3o3b3o25b3o$224b2o5b4o4bo2bo14bo106bo3bo143bo138b2o5b2o$232b4o
3bo271b3o137b2o5b2o$235bo3bo17bo105b2o3b2o140b5o$199bo39bobo14b2o251b
2o3b2o$181bo15bo3b2o9b2o25bobo5b2o6b2obo15b2o228bo147bo5bo$181b2o13b2o
bob2o9bobo7b2o16bo6b2o7bobo15b2o92b2o5b2o48bo77bobo103b2o40b3o3b3o$
176b2o4b2o11b2o6bo10bo7b2o33b2o107bo4bo3b3o47b2o64b2o10b2obo102b2o40bo
b2ob2obo$172b2o2b2o4b3o11b2obob2o9b3o156bo5b2obo5b2o36bobo64b2o10b2ob
2o3b3o136b2o7b2o$172b2o2b2o4b2o13bo3b2o34b2o3b2o121bo6bo4bo2bo5b2o19bo
5bo89b2obo4b3o25b2o5b2o102b2o7b2o$181b2o16bo37bo5bo121bobo9b2obo25b3o
3b3o13b2o5b2o29b2o35bobo33b2o5b2o61bo40b3o5b3o$181bo90b2o57b2o5b2o35b
3o27b2ob2ob2ob2o12b2o5b2o29b2o36bo103b3o41b3ob3o$212b3o23bo3bo29b2o57b
2o5b2o35b2o27b3o7b3o96bo93bo3bo42bobo$195b2o17bo7b2o15b3o270bobo94bo
41bo2bobo2bo$195b2o15bobo7b2o182bo7bo191bo5bo37bo2bo3bo2bo$212b2o61bo
230b2o2bo5bo89bo5bo38b2o5b2o$274bo96b2o133b2o5bo31bobo59bo3bo$274bo47b
o48b2o137b2o3b2o28b2o61b3o$323bo89b2o13b3o3b3o109bo$317bo3b3o90b2o12bo
2bobo2bo28b3o153bo$186b5o48b2o29b2o3b2o38bobo95bo13bo3bobo3bo26bo3bo
86bo65bobo$185bob3obo47b2o32bo42b2o109b4o3b4o25bo5bo40b2o3b2o36b2o67bo
bo4b2o$186bo3bo79bo5bo151bo7bo26b2obob2o43bo40b2o66bo2bo3b2o$187b3o81b
2ob2o234bo5bo105bobo$188bo72b2o9bobo217b2obo125bobo$261bobo9bo192bo6b
2o12b3o2b2o2bo3b2o10bobo106bo$252b3ob2o4b3o8bo191bobo5b2o13b2o6bo3b2o
11bo$252b4o2bo4b3o143b2o5b2o47bobo21b3o3b2o$187b2o67b2o4b3o100bo5bo89b
2o3bo23bo3bo112b3o$187b2o72bobo100b3o3b3o35bo9bo16bo24b3o11bo5bo25bo7b
o72bo19b3o4b2o$261b2o100b2ob2ob2ob2o34bo3bobo3bo15b3o13b2o5bob2o5b2o6b
o5bo9bo3bo10bobo5bobo69bobo18bo3bo3b2o34bo$362b3o7b3o33bo3bobo3bo14bo
3bo12b2o5bo2bo4bo2bo20b3o3b2o11bo3bo65b2o4bobo18bo5bo37bo$409bobo3bobo
15b2ob2o19bob2o5b2o2b2o11b2o3b2o6bo3b2o3bo2bo3bo2bo43bo18b2o3bo2bo19b
2ob2o38b3o$318bo45bo7bo37bo5bo16b2ob2o22b3o24b3o2b2o2bo3b2o4bobo3bobo
43bo25bobo$267b2o25b2o20bobo142b2o11bo5bo11b2obo12b2ob2o45b3o24bobo18b
2ob2o$267b2o24bobo21b2o114b2ob2o36bo5bo24b2ob2ob2ob2o52bo18bo17bo5bo
42b2o5b2o$292b3o4b2ob3o128b2ob2o67b2o2bobo2b2o50b2o38bo3bo42bo2bo3bo2b
o$291b3o4bo2b4o123b2o3bo3bo68b3o3b3o52b2o9b2o18b3o6b3o46b2ob2o224b2o$
283bo8b3o4b2o42bo84b2o4b3o43b2o25bo5bo64b2o17bo3bo5b3o45bobobobo223b2o
$283bo9bobo48bo90bo44b3o113bo5bo52bobobobo243b2o5b2o$282bobo9b2o46b3o
130b2o5b2obo110bo5bo50bo9bo240bo2bo3bo2bo$281b2ob2o188bo2bo4bo2bo5b2o
106bo52bo11bo239bo9bo$268bo5bo5bo5bo188b2o5b2obo5b2o13b2o5b2o82bo3bo
36bo265bo2bo3bo2bo$267b3o3b3o7bo17b2o61b2o5b2o58b2o47b3o23b2o5b2o83b3o
37bobo15b2ob2o243b2ob2ob2ob2o$266bo2b2ob2o2bo3b2o3b2o14b2o40bo20b2o5b
2o36b2o5b2o13b2o43bo3b2o117bo29b2o7b2o14bo2bobo2bo245bobo$266b3o5b3o
67bo64b2o5b2o57bobo128b2o7b2o12b2o23b3o3b3o244b2ob2o$342b3o107b2o5b2o
14bobo128bob2o3b2obo$282bo21bo127bo19b2o5b2o15bo101bo19b2o6bo3bobo3bo$
282bo20bo127bobo84bo58b3o18b2o6b2o2bobo2b2o11bo25b2o5b2o220b2o3b2o$
281bo21bo126bo3bo83bobo55b5o26b3o3b3o11bobo24b2o5b2o$430b5o38b2obob2o
38b2o55b2o3b2o6bo19bo5bo13bo239bo5b2o8bo3bo16b3o3b3o$347bo81b2o3b2o37b
o5bo96b5o5bobo36b3o12bo2bob2obo2bo214bo3bo3b3o8b3o16bo9bo$283b2o14b2o
3b2o39bobo82b5o39bo3bo97bo3bo3b2o12b2o25bo14b4ob2ob4o218bo5b2obo5b3o
16bo3bobo3bo$283b2o17bo36bo6b2o83b3o18b3o3b3o14b3o99bobo4b2o12b2o40bo
2bob2obo2bo213bo5bo4bo2bo25b3o3b3o8b2o$299bo5bo31bobo92bo18bo2bo3bo2bo
116bo5b2o279b2o9b2obo26bo5bo9b2o$300b2ob2o33b2o111bo3bobo3bo124bobo
285b3o$290b2o9bobo117bo28b2obobobobob2o125bo18b2o5b2o258b2o$290bobo9bo
116bobo28b2ob2o3b2ob2o144b2o5b2o306b3o$281b3ob2o4b3o8bo48bo65b2o32b3o
5b3o268b2o18bobo169b3o$281b4o2bo4b3o54bobo59b2o4b2o310bobo17bo2bo$285b
2o4b3o56b2o59b2o4b2o139bo24b2o29bo113b3o17b2o11bo$267b2o5b2o14bobo126b
obo53b2o81bobo22b2o28bobo7b2o18b4o5b6o69b3o16b2o3bo9bo$267b2o5b2o14b2o
129bo20bobo30b2o70b2o12b2o5bo43bob2o6bobo18bob2o7b4o61bo8b3o17b2o5b2o
163b2o3b2o$371bo73bo101b2o12b2o4bobo36b2o3b2ob2o8bo18bo7bob2o64bo9bobo
5b2o3b2o5bo2bo4bo163b5o$372bo68bo3bo7bo55bo51b2o3bo3bo35b2o4bob2o28b2o
5b2o65bobo9b2o5bobobobo6bobo169b3o$370b3o72bo6bobo54bobo46bobo5b5o42bo
bo101b2ob2o17bobo181bo$296b2o25b2o117bo2bo5bo3bo53b2o47bo6b2o3b2o42bo
29b2o5b2o63bo5bo16bobo170b2o$296b2o24bobo118b3o5b5o110b5o72bo7bob2o64b
o20bo171b2o$321b3o4b2ob3o116bobobobo90b2o18b3o50b2o7b2o12bob2o7b4o58b
2o3b2o35b2o3b2o$320b3o4bo2b4o117bo3bo91b2o19bo60b2o12b4o5b6o51b2o49b3o
8bobo$312bo8b3o4b2o378bobo48bo3bo6bo2bo$312bo9bobo126bo3bo56bo194b3o4b
2o3bo40bobo6b2o6b2o137b2o$311bobo9b2o125bobobobo53b2o64b3o3b3o121b3o4b
o2b3obo40bo5b2o3bo3bo2bo49b2o76bo8b2o$310b2ob2o136b5o3b2o50b2o62bo3bob
o3bo33b2o3b2o81b3o4b2ob2obo48b2o6b2o50b2o75bo5bo6b2o$309bo5bo135bo3bo
3b2o113bo3b2ob2o3bo33b5o83bobo8bo50bo2bo3b2o127bob2o3bo5b3o$312bo139bo
bo61bo57bob2o5b2obo33b2ob2o84b2o37bo22bobo3bo129b6o6b2o$309b2o3b2o13b
2o122bo61bo60bo7bo35b2ob2o121b3o27bobo129b4o4b2o$329b2o184b3o103b3o
121bo30bobo137b2o$200b2o5b2o253bo104b2o164b2o10b2o30bo$200b2o5b2o102bo
142bo6bobo103b2o144b2o19bo31b2o136b2obob2o$296b2o5b2o6bo18bo122bobo3b
2o3bo80b5o163b2o19bobo4b2o23b2o61bo$295bo2bo3bo2bo4bo18bobo121bobo3b2o
3bo9b2o68bob3obo7bo176b2o4b2o31b2o3b2o47b3o73bo5bo$298b2ob2o25bo3bo
121bo4b2o3bo9b2o69bo3bo5b4o144bo70bobobobo46b5o$297bobobobo24b5o128bob
o82b3o5b4o9b2o52b2o79b3o70b5o46bobobobo72b2ob2o$297bobobobo8b2o13b2o3b
2o128bo84bo6bo2bo9b2o52b2o78b5o70b3o47b2o3b2o74bo$295bo9bo6b2o14b5o
118b2obob2o96b4o5bo136b2o3b2o6b3o3b3o55bo$294bo11bo22b3o119bo5bo97b4o
4bo137b5o7bo2bobo2bo91b2obo$216b2o112bo121bo3bo101bo17b2o5b2o116bo3bo
6bo3bobo3bo71b2o12b3o2b2o2bo3b2o6bo$216b2o80b2ob2o150b3o120b2o5b2o117b
obo8bo2bobo2bo72b2o13b2o6bo3b2o5bobo$296bo2bobo2bo14bo383bo11bo3bo90b
3o3b2o10bobo76b2o$296b3o3b3o12bobo393b2o5b2o38bo5bo44bo3bo13bo3bobo71b
2o$309b2o4b2o209bo25b2o158b3o5b3o36b3o3b3o60b2o3bo2bo$200b2o5b2o100b2o
4b2o89bo119b4o22b2o149b2o7b3o5b3o35b2o2bobo2b2o7b2o33bo3bo12b2o6b2o6b
2o$199bo2bo3bo2bo86b2o5b2o10b2o90b2o107b2o9b4o172b2o52bob4ob4obo6b2o
32b3o3b2o9bo2bo3bo3b2o4b2o$200bo2bobo2bo87b2o5b2o12bobo86b2o108b2o9bo
2bo6bo87b2o132b3o3b3o26b2o13b2o6bo10b2o6b2o$203bobo9b3o101bo201bo5b4o
5b3o6b3o3b3o71b2o131b3o5b3o25b2o12b3o2b2o2bo15bo2bo$201b3ob3o6bo3bo
235b2o65bo4b4o5bo3bo5bo2bobo2bo259b2obo16bobo$199b3o5b3o121bo122b2o70b
o7bob3obo6b2ob2o$199b2o7b2o3bo5bo110bobo156bobo43b5o$199b2o7b2o3b2o3b
2o104b2o3bo3bo17bo137b2o52bo11bo$200bob2ob2obo15b2o98b2o3b5o17bobo57bo
78bo53bo9bo$200b3o3b3o13bo3bo101bobobobo19b2o4b2o50bo133bobobobo115b2o
$201bo5bo8bo4bo5bo101bo3bo20b2o4b2o48b3o133bobobobo115b2o$215bobo2b2ob
o3bo8b2o66b2o48b2o191b2ob2o$215bobo3bo5bo8b2o66b2o23bo3bo17bobo50bo
139bo2bo3bo2bo68b2obob2o$200b2o14bo5bo3bo101bobobobo16bo53bo59bo79b2o
5b2o$146b2o52b2o22b2o103b5o69b3o57b2o158bo5bo83b2o5b2o37b2o5b2o$146b2o
181bo3bo6bo123b2o247b2o5b2o37b2o5b2o88bo$330bobo6b3o282b2ob2o227b3o$
331bo6b5o193b2o88bo6b2o2b2o4bo2b2o12b2o197bo$197b2o138b2o3b2o192b2o95b
2ob2o6b2obo12b2o196b2o$196bo3bo5bo96b3o32b5o294bobo6bo22bo$185b2o8bo5b
o3bobo94bo3bo31bo3bo118bobo159bo14b2o4b3o21b3o$185b2o8bo3bob2o2bobo
131bobo119b2o159bobo42b5o$195bo5bo4bo94bo5bo32bo121bo147b2o9bo3b2o11b
2o4b3o19b2o3b2o$196bo3bo100b2o3b2o15b3o5b3o83bo192b2o9bo3b2o10bobo6bo
20b5o$147bo49b2o94bo2bo25b2ob2o3b2ob2o80bobo203bo3b2o9b2o6b2obo12b2o5b
o3bo$146b3o54b2o3b2o73b3o7bo28b2obobobobob2o5b2o74b2o204bobo12b2o4bo2b
2o12b2o6bobo$145b5o53bo5bo59b2o11bo4bo9bo6bo18bo3bobo3bo6b2o203b2o5b2o
69bo45bo$137bo6b2o3b2o86b2o30b2o10bo5bo8b2o5bobo13b2o2bo2bo3bo2bo211b
2o5b2o119b2o$137bobo5b5o54bo3bo11b2o15bobo7b2o33bo8bo11bobo13bo4b3o3b
3o340bobo$126b2o12b2o3bo3bo55b3o12b2o17bo7b2o34b2o8b2o10bo3bo7bobo348b
2o4b3o7b2o$126b2o12b2o4bobo88b3o65bo3b4o4b2o348bo2bo4b3o6b2o$140b2o5bo
135b2o8b2o7bo2bo4b4o264b2o88b2o4b3o$137bobo142bo8bo3bo6bo2bo4bo2bo263b
2ob2o91bobo$137bo20b2o109b2o10bo5bo4bo2bo7b2o5b4o264b4o91b2o$159bo77b
3o29b2o11bo4bo4bo2bo13b4o11b2o5b2o246b2o$159bobo58b2o17bo43b3o7b2o14bo
14b2o5b2o$160bobo42b2o13b2o15bobo831bo$141b2o18bo3b2o38b2o30b2o831bobo
$141b2o22b2o129bo775b2o$295bo234bob2o272bob2o262bo$295b3o231b5o271b5o
221b2o38bobo$203bo325b2o3bo270b2o3bo218bo3bo2b2o13b3obobo9bo5bo$201bo
3bo326b2o274b2o218b2obob2o3b2o3b3obo8bo2bo3b3o2bo5bo$206bo325b2o274b2o
218bo5b3o3b2obo3b2o4bob2o2bobobo4b2o2bobo$201bo4bo328b4o272b4o213bob5o
b2ob2o3bo6b2o10bobo8bo$202b5o327bo3bo271bo3bo213bo7bo4b2o4bo3bo13b3ob
5o$167b2o52b4o308b2o2b2o270b2o2b2o211b3o4b3o4b2o3b3o3bo2b2o14b2o$157b
3o6b2o52bo3bo304bo2bo3bo268bo2bo3bo100b2o110bo8bo4bobobob2obo3b4o2bo
11bo$157b3o8bo55bo304b7o269b7o101b2o111b6obo3bo5bobo7bo3bobo$158bo61bo
2bo808b3ob3o2b3ob2o2b2ob2o3bo2bo$158bo42b4o324b7o269b7o101b2o111b6obo
3bo5bobo7bo3bobo$141b2o5b2o8bo26b2o14bo2b2o323bo2bo3bo268bo2bo3bo100b
2o110bo8bo4bobobob2obo3b4o2bo11bo$141bob2ob2obo7bobo25b2o15bo2b2o33b2o
291b2o2b2o270b2o2b2o211b3o4b3o4b2o3b3o3bo2b2o14b2o$142bobobobo53bo2bo
33bo2bo6bo284bo3bo271bo3bo213bo7bo4b2o4bo3bo13b3ob5o$142bobobobo54b2o
37bo5b3o284b4o272b4o213bob5ob2ob2o3bo6b2o10bobo8bo$141bo7bo7bobo82bo5b
ob2o280b2o274b2o218bo5b3o3b2obo3b2o4bob2o2bobobo4b2o2bobo$158bo44b2o
35bobo6b3o280b2o274b2o218b2obob2o3b2o3b3obo8bo2bo3b3o2bo5bo$158bo20bo
22bo2bo34bobo6b2o21bo256b2o3bo270b2o3bo218bo3bo2b2o13b3obobo9bo5bo$
158bo19b2o5b2o15bo2b2o5b2o27bo30bobo254b5o271b5o221b2o38bobo$143b2ob2o
9b3o18bobo4b2o14bo2b2o6b2o59bobo254bob2o272bob2o262bo$141bo2bobo2bo7b
3o41b4o55b2o11bo2bo795b2o$141b3o3b3o88b2o3b2o15b2o11bobo794bobo$142bo
5bo89bo5bo27bobo796bo$272bo61b2o5b2o$141b2o5b2o44b3o3bo38bo3bo90b2o5b
2o$141b2o5b2o42b5o2bobo12b2o12b2o10b3o289b4o140bo$187bo3b2o3b2o3bo12b
2o10bo3bo45bo255bo3bo139b4o$182bo3bo4b3o3bo2bo24bo5bo44bo255bo137b2o5b
4o$167b2o12bo8bob2o3b3o20b2o2b2obo3bo43bobo255bo2bo132bo2bo4bo2bo5b2o$
167b2o12bo2b2o5bo28b2o3bo5bo42b2ob2o390bo2bo4b4o5b2o$182b2o5bo2b2o3b3o
26bo3bo42bo5bo392bo3b4o$183b3o3b5o3bo2bo27b2o46bo305b2o88bo3bo$191b2o
3b2o3bo12b2o57b2o3b2o70b2o230b2o34bo18bob2o29bobo$183b3o3b8o2bobo12b2o
134b2o64b2o119b2o5b2o67bo4b4o14bo2b2o2b3o12b2o10bobo$182b2o5bo2bob3o3b
o214bobo119b2o5b2o67bo5b4o13bo6b2o13b2o11bo$167b2o12bo2b2o5bo43b2o26b
2o12bo139bo190b2o9bo2bo13b2o3b3o$167b2o12bo8b2o43b2o25bo3bo10bo57bo5bo
8bo111bo145b2o9b4o15bo3bo$182bo3bo74bo5bo3b2o5bo55b3o3b3o6bobo109b2o
155b4o46b2o3b2o$187bo73bo3bob2o2b2o60bo3bobo3bo4bo3bo108bobo154bo19bo
3bo25bo5bo$235b3o3b3o17bo5bo65bo9bo4b5o283b2o3b3o$235bo2bobo2bo18bo3bo
8b2o57b3o3b3o4b2o3b2o277b2o3bo6b2o13b2o9bo3bo184b2o$237b2ob2o8b3o10b2o
10b2o71b5o278b2o3bo2b2o2b3o12b2o10b3o186bo$249bo3bo95b3o176b2o50b2o3b
2o50bob2o215b3o$233bo11bo104bo113b2o62b2o93b3o230bo$234bo9bo3bo5bo148b
3o57b2o116bo3bo36bo3bo$236bobobobo5b2o3b2o81b2ob2o20bo43bo59bo116b3o
11bob2o$236bobobobo94bobo21bobo40bo177b3o5b2o3bo2b2o2b3o12b2o2bo5bo$
237b2ob2o91b2ob2ob2ob2o20b2o224b2o3bo6b2o13b2o2b2o3b2o$234bo2bo3bo2bo
6bo81bo2bo3bobo21b2o4b2o38b3o182b2o3b3o67b2o$235b2o5b2o6bobo80bo7bo22b
2o4b2o40bo116bo6b3o5b3o33bo16bo3bo68b2o$250bobo80bo2bo24bobo47bo81b2o
33b3o4b2ob2o3b2ob2o31b4o41bo$250bo83b2o25bo130b2o34b3o4b2obobobobob2o
19b2o9b2obobo13bo3bo21bobo$250bo243bo41bo3bobo3bo20b2o8b3obo2bo10b2o3b
3o20bobo$250bo2bo272b2o3b2o3bo2bo3bo2bo31b2obobo11bo6b2o13b2o6bo$251b
2o235b2o36b2o3b2o4b3o3b3o33b4o12bo2b2o2b3o12b2o6bo$329bo158bobo29bo59b
o15bob2o22bo2bo$306b2o5b2o12bobo158bo30b2o102b2o$306b2o5b2o10b2o191b2o
4b2o3bo$319b2o4b2o181b2o7b3o4b2o2bobo$319b2o4b2o181b2o8b2o4b2o2bobo$
327bobo189b2o8bo14b2o361b2o$329bo157bo32bo23b2o361b2o$235b2o5b2o149b2o
91b2o112b2o3bo2bo3b2o$235b2o5b2o96bo53b2o90bobo97bo13b5o4b5o$339b3o51b
o174b2o5b2o9b3o11b2o3bo2bo3b2o$322b2o14b5o205bo19b2o5b2o12bo$322b2o13b
2o3b2o195bo8b2o38bobo4bo19b2o5b2o283bo$306b3o3b3o23b5o195bobo2b2o4b2o
18bo5bo13bo4b2o19b2o5b2o281b2ob2o$305bo2bo3bo2bo22bo3bo195bobo2b2o4b3o
7b2o7b3o3b3o17bobo$309bobo8bo18bobo197bo3b2o4b2o8b2o7bo2bobo2bo327bo5b
o$309bobo9bo18bo207b2o20b2ob2o15b2o$309bobo9bo226bo41b2o312b2obob2o$
305bo2bo3bo2bo220b2o3b2o$306bo7bo24b2o171b2o22b2o3b2o16b2o355b2o$319b
2o3b2o13b2o171bobo44b2o7bo7bo331b4o4b2o$322bo189bo25b3o28bobobobo331b
6o6b2o$319bo5bo212b3o28bobobobo330bob2o3bo5b3o$313bo6b2ob2o214bo28bob
2ob2obo329bo5bo6b2o$311b2ob2o5bobo9b2o233b2o5b2o29b2o299bo8b2o$322bo9b
obo48b3o174bo44b2o309b2o$311b2ob2o6bo8b3o4b2o45bo174bo46bo$311bo3bo14b
3o4bo2b4o40bo174bobo52b3o5b3o$312b3o16b3o4b2ob3o214b2ob2o51b3o5b3o$
306b2o24bobo108b3o93b2o16bo5bo51b2o5b2o288b2o$306b2o25b2o107bo2bo93b2o
19bo56bo3bo290b2o$445bo111b2o3b2o51bo2bobo2bo299bo$441bo3bo104b2o62bo
3bobo3bo297b3o$445bo103bobo63bo2bobo2bo297b5o$277b2o5b2o14b2o140bobo
103b3o4b2o3bo54b3o3b3o296b2o3b2o$277b2o5b2o14bobo151b2o83b2o6b3o4bo2b
3obo$295b2o4b3o46b2o102b2o83b2o7b3o4b2ob2obo$291b4o2bo4b3o44bobo197bob
o8bo14b2o$277b3o3b3o5b3ob2o4b3o8bo38bo198b2o23b2o36bo5bo302b3o$277bo2b
obo2bo14bobo9bo141bo157b3o3b3o301b3o$279b2ob2o16b2o9bobo139bobo155bo2b
2ob2o2bo252b2o$310b2ob2o137bo3bo154bo3bobo3bo252b3o$275bo11bo21bo5bo
58b2o5b2o69b5o122b2o32bobobobo245b2o9b2obo26bo5bo9b2o$276bo9bo6b2o17bo
33b2o26b2o5b2o68b2o3b2o112bo8bobo283bo5bo4bo2bo25b3o3b3o8b2o$278bobobo
bo8b2o14b2o3b2o29bobo104b5o112bob2ob2o4b3o27b2ob2o3b2ob2o247bo5b2obo5b
3o16bo3bobo3bo$278bobobobo62bo105b3o42b2o5b2o62bob3o2bo4b3o6b2o20bo7bo
245bo3bo3b3o8b3o16bo9bo$279b2ob2o49b2o119bo43b2o5b2o11b2o50bo3b2o4b3o
7b2o276bo5b2o8bo3bo16b3o3b3o$276bo2bo3bo2bo4bo21bo20b2o182bobo58bobo$
277b2o5b2o6bo20bo19bo131bo52bo60b2o302b2o3b2o$292bo21bo150bobo99b2o3b
2o$342b3o123b2o4b2o94bo$344bo123b2o4b2o91bo5bo333b2ob2o$290b2o3b2o14b
2o30bo124b2o98b2ob2o335bobo$293bo17b2o152bobo101bobo332b2ob2ob2ob2o$
290bo5bo168bo104bo333bo2bo3bo2bo$291b2ob2o80bo3bo189bo333bo9bo$292bobo
9b2o36b3o31bo3bo523bo2bo3bo2bo$293bo9bobo21bo16bo560b2o5b2o$293bo8b3o
4b2o16b2o14bo115b2o39b2ob2o380b2o$301b3o4bo2b4o11bobo44b2obo3bob2o75b
2o38bo5bo106b2o5b2o264b2o$302b3o4b2ob3o59b3o3b3o187b2o40b2o5b2o$277b2o
24bobo69bo5bo116bo7bo63b2o$277b2o25b2o192bo2bobo2bo$453bo5bo38b3o3b3o$
452b3o3b3o$246b2o5b2o196b2o2bobo2b2o97b3o$246b2o5b2o16b2o178b2ob2ob2ob
2o97bo$271bobo180b2ob2o101bo$266b2o4b3o177bobo3bobo$262b4o2bo4b3o105b
2o68bo2bo3bo2bo$262b3ob2o4b3o8bo97b2o37bobo31bo3bo16b2o$271bobo9bo136b
o2bo27bobo5bobo13b2o158b2o5b2o$271b2o9bobo126b2o10b2o27bo7bo37b2o135b
2o5b2o$281b2ob2o125b2o8bo3b2o5bo65b2o$262b2o16bo5bo54b2o5b2o35bo30b2o
5b2o6bobo42bo77b2o$262b2o19bo32b2o23b2o5b2o33bobo29bo4bo2bo6bo3bo40bob
o75b2o$280b2o3b2o28bobo58bo5bobo35bobo8b3o40bo3bo76bo$246bo7bo62bo3b3o
51b3o3bo2bo11b2o31b2o3b2o38b5o15bo$192b2o50bob2o5b2obo66bo50bo3bo3bobo
11b2o75b2o3b2o14bobo34b2o5b2o6bo$192b2o50bo3b2ob2o3bo27bo37bo53bo6bobo
88b5o18b2o5bo26b2o5b2o5b2o$245bo3bobo3bo28bo88bo5bo5bo89b3o5b2o12b2o4b
obo39bobo78b2o$246b3o3b3o30bo87bo5bo96bo6b2o12b2o3bo3bo119b2o$374bo3bo
115bobo5b5o$193bo68bo78b3o3b3o25b3o116bo6b2o3b2o$192bobo66b3o18b2o56bo
2bo3bo2bo151b5o$191bo3bo64b5o17b2o56b2obo3bob2o101b2o5b2o42b3o129bo7bo
$192b3o64b2o3b2o186b2o5b2o43bo129bobo5bobo$190b2o3b2o73bo138b2o5b2o
219bo3bo$269bobo137b2o5b2o13b2o49b2o150bo2bo3bo2bo$268bob2o159b2o48bob
o151bobo3bobo$261b3o3b2ob2o10b2o196b3o4b2ob3o144b2ob2o$261b3o4bob2o10b
2o195b3o4bo2b4o113b2o18b3o5b2ob2ob2ob2o$208bo3b2o32b2o21bobo104b2o102b
3o4b2o42b3o3b3o67bo17bo3bo4b2o2bobo2b2o$200b2o4b2obob3o13b2o17b2o22bo
105b2o103bobo47bo2bobo2bo67bobo6bobo5bo5bo4b3o3b3o$200b2o4bo4b3o13b2o
113bo85b2o52b2o47b2obobob2o68b2o6bo3bo4bo3bo6bo5bo$206bo3bo129b2ob2o
83b2o73b2o26b2o5b2o80bo5b3o$185b2o20b3o130b2ob2o158b2o111bo4bo4b3o$
183bo3bo56bo375bo$177b2o3bo5bo18b3o33bobo72b2o5b2o12bobobobo113b2o155b
o3bo21b2o$177b2o2b2obo3bo17bo3bo32b2obo4b3o64b2o5b2o81b3o5b3o40bobo15b
2o4bo2b2o12b2o114bobo23b2o$182bo5bo17bo4b3o13b2o2b2o10b2ob2o3b3o86b2ob
2o64b3o3b3o11bo5bo18b2o4b3o13b2o6b2obo12b2o31b2ob2o$183bo3bo18b2obob3o
13b2o2b2o10b2obo94b3o4b2o57bob4ob4obo8b3o3b3o13b4o2bo4b3o13bobo6bo44bo
2bobo2bo$185b2o21bo3b2o29bobo96bo5b2o58b2o2bobo2b2o8bo2b2ob2o2bo12b3ob
2o4b3o15b2o4b3o44bobo3bobo127b2o5b2o$244bo164b3o3b3o9bo3bobo3bo21bobo
69b3o3b3o106bobo18b2o5b2o$249b2o3b2o154bo5bo12bobobobo23b2o17b2o4b3o
44b2o111bo3bo$250b5o222bobo6bo44b2o111bo$251b3o98b2o72b2ob2o3b2ob2o34b
2ob2o6b2obo12b2o29b2o103b3o4bo4bo8b2o$252bo99b3o73bo7bo36b2o2b2o4bo2b
2o12b2o134b3o5bo12b2o$342bobo9b2obo277bo3bo4bo3bo$342bo6bo4bo2bo5b2o
269bo5bo5bobo$348bo5b2obo5b2o160bo109bo3bo$320b2ob2o18bo4bo3b3o111bo
56bobo110b3o19b2o$320b2ob2o20b2o5b2o111b3o54bobo133b2o$193b2o5b2o118b
2ob2o139b5o47b2o3bo2bo$193b2o5b2o116bob2ob2obo136b2o3b2o46b2o4bobo$
209bobo39b2o65b3o3b3o13b2o3b2o117b5o54bobo143bo3bo$210b2o39b2o66bo5bo
138bo3bo56bo143bo3bo$210bo130bo3bo119bobo$342b3o61b3o3b3o51bo69b3o$
342b3o60bo2bo3bo2bo3bobo113bo3bo126b2obo3bob2o$409bobo8b2o112bo5bo126b
3o3b3o$409bobo8bo7b2o5b2o29b2o66bo5bo96b2o17b2obob2o5bo5bo$209b2o198bo
bo16b2o5b2o29b2o69bo99b2o$208bobo194bo2bo3bo2bo119bo3bo116bo5bo$207b3o
133b2o61bo7bo121b3o108b2o$207b2o116b2o16b2o192bo102b3o4b2o8b2ob2o$194b
o5bo6b2o116b2o312b5o6b2o7bo$193b3o3b3o6bobo427bobo3bo5b3o$192bo3bobo3b
o6bo326b2o100b2o3bo6b2o$192bo9bo333b2o109b2o25b2o$193b3o3b3o126bo102bo
151b2o5b2o55b2o25b2o$206b2o3b2o107bo6bobo102b2o149b2o5b2o$206b2o3b2o
106bobo3b2o3bo100b2o$283b2o5b2o27bobo3b2o3bo9b2o355b2o5b2o$208b3o72b2o
5b2o28bo4b2o3bo9b2o64b2o5b2o265b2o15b2o5b2o$195b2ob2o8b3o10bo105bobo
76b2o5b2o265b2o4b3o$196bobo10bo10b2o106bo348b2o6b5o$192b2ob2ob2ob2o16b
2o3b2o91b2obob2o352b3o5bo3bobo$192bo2bo3bobo16b3o96bo5bo345bo7b2o6bo3b
2o$192bo7bo18b2o97bo3bo344b2ob2o8b2o$192bo2bo24b2o5b2o90b3o358b2o$193b
2o26bo5bobo436bo5bo$229bo212bobo5b2o236b2o$229b2o212b2o5b2o214b2obob2o
15b2o$284bo5bo152bo$187bo95b3o3b3o397bo$165b2o5b2o13b2o93b2o2bobo2b2o
159bo235bobo$101b2o5b2o55b2o5b2o8b2o4b2o91bob4ob4obo157bobo128b3o5b3o
95bobo$101b2o5b2o68b2o2b2o4b3o92b3o3b3o28b2o108b2o6b2o12bo129bo2b2ob2o
2bo96bo$178b2o2b2o4b2o92b3o5b3o27b2o106bo4bo2bo4bo11b3o127b3o3b3o104b
3o5b3o$187b2o10bo228bo4bo2bo4bo13bo128bo5bo104b2ob2o3b2ob2o$187bo10b3o
227bo4bo2bo4bo244b2obob2o2b2obobobobob2o$101b3o3b3o88b3o229b2o6b2o228b
2o16bo5bo3bo3bobo3bo$100bo2bo3bo2bo557b2o17bo3bo4bo2bo3bo2bo$104bobo
89b2o3b2o81bo403b3o6b3o3b3o$100b2o7b2o70b2o13b2o3b2o80bobo390bo$100b2o
7b2o6b2o62b2o77bo21b2ob2o388bobo$103bo3bo9b2o138b4o4bo16b2ob2o296b2o
88b2o3bo$103b2ob2o9b2o80bo56b4o5bo169bo3bo23bo119b2o83b2o3b2o3bo$101b
3o3b3o7bo48bo5bo6bo18bobo55bo2bo9b2o12b3o137b2o9bo5bo20bobo204b2o3b2o
3bo$101b2o5b2o6bobo46b3o3b3o6bo19b2o54b4o9b2o13bo5b2o131b2o15bo18b2o
131b3o80bobo26b2o$101bo7bo6bobo45bo3bobo3bo5bo19b2o48b2o5b4o23bo5b2o
143bo3b2o18b2o12b2o119bo81bo27b2o$117bo46bo9bo24b3o47bobo8bo175b3o20b
2o12b2o102b2o14bo$165b3o3b3o24bobo48bo211bobo106b3o4b2o140b2o$108bo69b
2o3b2o13b2o48b2o186b3o24bo105b5o6b2o137bo$108bo5b2o3b2o60bo112b2o139bo
3b2o127bobo3bo5b3o78bobo48bo4bobo$114bobobobo57bo5bo100bo8b2o127b2o15b
o9b2o116b2o3bo6b2o7bo70bo50bobo3b2o$115b5o59b2ob2o100bo5bo6b2o124b2o9b
o5bo9b2o125b2o8b2ob2o68bo49bo3b2o$105b2o3b2o4b3o48b2ob2o8bobo9b2o90bob
2o3bo5b3o5b2o128bo3bo17b3o117b2o81bo2bo46bo3b2o$117bo12bo37bobo10bo9bo
bo91b6o6b2o6b2o279bo5bo67b3o47bo3b2o$129b4o31b2ob2ob2ob2o6bo8b3o4b2o
87b4o4b2o161bobo251bobo$128b2obobo30bo2bo3bobo15b3o4bo2b4o91b2o160b5o
125b2obob2o30b2o5b2o80bo$127b3obo2bo2b2o25bo7bo17b3o4b2ob3o252b2o3b2o
161b2o5b2o66b3o$128b2obobo3b2o25bo2bo23bobo38b2o5b2o41b2obob2o166b2o3b
2o235bo3bo27b2o5b2o$101b2o2b2o3b2o17b4o32b2o25b2o38b2o5b2o418b3o34bo5b
o26b2o5b2o$101b2o27bo151bo5bo372bo34b2obob2o$458bo201bo$108bo26b2o5b2o
139b2ob2o168b2o$108bo26b2o5b2o15b2o124bo413bo29b3o3b3o$94bo64bobo293bo
242bobo27bo2bo3bo2bo$92b4o58b2o4b3o425b2o69b2o37bobo31bobo$91bobob2o
53b4o2bo4b3o292bo2bo128b2o68b2o39bo28b2o7b2o$86b2o2bo2bob3o37b3o3b3o6b
3ob2o4b3o8bo286b2o200bo59b2o6b2o7b2o$86b2o3bobob2o37bo2bo3bo2bo14bobo
9bo113b2o336b3o3b3o67b2o19b2o9bo3bo$92b4o42bobo18b2o9bobo59b3o3b3o44b
2o335bo3bobo3bo66b2o30b2ob2o$94bo12bo26b2o7b2o24b2ob2o57bo2bo3bo2bo
379bo3b2ob2o3bo95b3o3b3o$106b3o25b2o7b2o6b2o15bo5bo60bobo383bob2o5b2ob
o95b2o5b2o$105b5o27bo3bo9b2o18bo63bobo385bo7bo97bo7bo$104bobobobo26b2o
b2o26b2o3b2o60bobo$104b2o3b2o24b3o3b3o87bo2bo3bo2bo$135b2o5b2o88bo7bo
489bo$135bo7bo7bo18bo559bo$107bo42b3o17bo513b3o$106bobo40bo3bo15bo7bob
o449b3o52bo35b3o$106bobo33bo5bob3obo25bo52bo395bobo53bo33bo3bo3b2o3b2o
$107bo34bo6b5o26bo50b2ob2o392bo3bo77bobo5bo5bo$106b2o63b2o4bo2bo447bo
3bo77bo3bo4bo3bo$106b2o63b2o5b3o50b2ob2o478bo5b3o$106b2o31b2o3b2o85bo
3bo387b2o4b3o68b2o8bo4bo4b3o$161bo70b3o388b2o75b2o12bo$156bo4b4o74b2o
469bo3bo12b2o3b2o2b2o$156bo5b4o73b2o469bobo23b2o$162bo2bo5b2o$162b4o5b
2o30b2o5b2o407bo110bo$135b2o2b2o3b2o15b4o38b2o5b2o404b4o110bo28b2o5b2o
$135b2o24bo82bobo368b4o121bobo16b2o5b2o$243bo2bo4bo356b2o5bo2bo38b2o5b
2o72bo3bo$142bo99b2o5b2o357b2o5b4o5bo31bo2bo3bo2bo71bo$142bo91bo5b2o3b
o8b2o360b4o4bo31bo9bo63b3o4bo4bo8b2o$131bo101bobo6b2o10b2o363bo36bo2bo
3bo2bo63b3o5bo12b2o$128b4o100bo3bo6bo2bo409b2ob2ob2ob2o62bo3bo4bo3bo
16b3o3b3o$127b4o102b3o8bobo413bobo65bo5bo5bobo16bo2bobo2bo$120b2o5bo2b
o100b2o3b2o421b2ob2o65bo3bo24bo3bobo3bo$120b2o5b4o5bo490b5o98b3o17b2o
7bo2bobo2bo$128b4o4bo66b3o3b3o414bob3obo117b2o9bo3bo$131bo70bo2bo3bo2b
o414bo3bo127b2o5b2o$206bobo419b3o127b3o5b3o$184b3o19bobo420bo27b3o3b3o
85bo6b3o5b3o$161bo22bo21bobo447bo9bo83bobo$139b5o17b2o22bo16bo2bo3bo2b
o443bo3bobo3bo23b3o56bo3bo$138bob3obo15bobo40bo7bo445b3o3b3o24bo58b5o$
139bo3bo484b2o28bo5bo26bo56b2o3b2o$140b3o27b2o456b2o119b5o5b3o$141bo
27bobo62b2o494b2o18b3o6b3o$171bo32bo29b2o494b2o19bo6b5o$202b2ob2o550b
2o3b2o$740bo16b2o3b2o$140b2o60b2ob2o531bobo$140b2o28b2o30bo3bo529b2o$
169bobo31b3o524b2o4b2o$154b2o15bo38b2o518b2o4b2o19b2o3b2o$155b2o53b2o
470b2o5b2o47bobo16b2o3b2o2b2o$154bo527b2o5b2o49bo17b5o3b2o$657b2o100b
3o$126b2o43b2o5b2o477b2o100b3o$126b2o43b2o5b2o34bobo$212bo3bo555bo$
212bo519b2o38bobo$126b3o75b3o4bo4bo8b2o428bo76bobo40b2o$126b3o75b3o5bo
12b2o427b4o5bo68bo42b2o4b2o$203bo3bo4bo3bo436b2obobo3bobo110b2o4b2o$
202bo5bo5bobo425b2o8b3obo2bo2bobo107bobo$171b3o3b3o23bo3bo434b2o9b2obo
bo4bo108bo$124b2o3b2o40bo2bobo2bo24b3o447b4o$125b5o40bo3bobo3bo474bo
28b2ob2o72bo$126b3o41b4o3b4o479b2o3b2o17b2ob2o71b3o$127bo43bo7bo480bob
obobo17b2ob2o38bo31b5o$661b5o16bob2ob2obo35b2o30b2o3b2o$143b3o516b3o
17b3o3b3o35bobo30b5o$145bo3b2o512bo19bo5bo69bo3bo$144bo3bobo609bobo62b
2o$150bo567b2o41bo63b2o$717b2o$124b2o46bo32b2o512bo$125bo45b3o31b2o
554b2o$122b3o45bo3bo586b2o$122bo47b2ob2o487b2o$170b2ob2o487b2o$682b2o
140b3o$170b2ob2o507b2o139bo3bo$170b2ob2o$170bo3bo3b2o642bo5bo$171b3o4b
2o642b2o3b2o$172bo503bobo113b2o$676bo2bo111b4o7b2o$679b2o109bobobo6bo
2b2o11b2o6bo$182b2o493bo3b2o5bo101b2ob3o4b6o11b2o5bobo$173bo8bobo494b
2o6bobo103b2obo5b4o18bobo$172bobo2b2o6bo483b2o5bo2bo6bo3bo102b2obo29bo
3bo$172bobobo2bo2bo2bo7b2o473bobo5bobo8b3o136bo3b4o$173bo3b2o6bo7b2o
473bo16b2o3b2o101b2obo26bo2bo4b4o5b2o$134b2o5b2o39bobo482b2o54b2o5b2o
53b2o6b2obo5b4o17bo2bo4bo2bo5b2o$134b2o5b2o39b2o539b2o5b2o53b2o3b2ob3o
4b6o18b2o5b4o$170b2o3b2o613bobobo6bo2b2o24b4o$170b2o3b2o614b4o7b2o26bo
$171b5o8b2o5b2o599b2o$172bobo9b2o5b2o2$172b3o3$687b2o96bo$687b2o95b3o$
82b2o699b5o$82b2o89b2o607b2o3b2o$134b2o5b2o30b2o608b5o$134bob2ob2obo
41b3o3b3o590bo3bo$82b3o50bobobobo41bo2bo3bo2bo528b2o7b2o51bobo$82b3o
50bobobobo45bobo532bob2o3b2obo52bo$39b2o93bo7bo44bobo532bo3bobo3bo$38b
o2bo145bobo532b2o2bobo2b2o54b2o$41bo141bo2bo3bo2bo529b3o3b3o55bo$41bo
38b2o3b2o97bo7bo531bo5bo57b3o$39bobo39b5o50b2ob2o649bo$39bobo40b3o49bo
2bobo2bo$40bo42bo27b2o5b2o14b3o3b3o664b2o5b2o$111b2o5b2o15bo5bo43bo
619bo2bo5bo2bo$183b2ob2o$37b2o3b2o97b2o580b2o85bobo$37bo5bo97b2o40b2ob
2o535b2o80b2o3bobo3b2o$183bo3bo$38bo3bo141b3o622bo3bo$39b3o38b2o109b2o
$55bo3b2o20bo63b2o44b2o523bo$47b2o4b2obob3o13b2o2b3o64b3o566b4o$47b2o
4bo4b3o13b2o2bo56bobo9b2obo562bobob2o88b2o5b2o$53bo3bo77bo6bo4bo2bo5b
2o550b2o2bo2bob3o$34bo19b3o84bo5b2obo5b2o36b2o512b2o3bobob2o87bo9bo$
34b4o98bo4bo3b3o38bo5bo3bo517b4o88bo3bobo3bo$24b2o9b4o15b3o54bo7bo18b
2o5b2o38bobo3bo5bo518bo12bo76bo3bobo3bo$24b2o9bo2bo14bo3bo52bobo5bobo
64bobo2b2obo3bo8b2o520b3o76bobo3bobo$29bo5b4o14bo4b3o13b2o37bo3bo68bo
4bo5bo8b2o519b5o76bo5bo$29bo4b4o15b2obob3o13b2o34bo2bo3bo2bo12b2o3b2o
52bo3bo529bobobobo$34bo20bo3b2o50bobo3bobo74b2o530b2o3b2o39bo$113b2ob
2o16bo3bo44b2o3b2o582b2o$110b2ob2ob2ob2o14b3o45bo5bo577b2o4b2o$110b2o
2bobo2b2o14b3o591bo33b2o2b2o4b3o$111b3o3b3o64bo3bo539bobo32b2o2b2o4b2o
$112bo5bo66b3o540bobo41b2o8b2o$729bo42bo9bobo$728b2o54bo$136b2o590b2o
54b2o$118b2o16b2o590b2o31bo52b2o$118b2o621bo20bo3bo47b2o$741bobo13b2o
8bo12b2o$186b2o556b2o11bo5b2o2bo12b2o$186b2o542b2o12b2o11bobo5b2o$122b
2o606b2o12b2o12b2o3b3o52b2o$113b2o7bo2bo615bobo65bo8bobo$112bo4b2o7bo
614bo16b2o3b3o42bob2ob2o4b3o$112bo6bo6bo6b2o622bobo5b2o41bob3o2bo4b3o
6b2o$113b6o7bo6b2o618b2o2bo5b2o2bo12b2o27bo3b2o4b3o7b2o$122bo2bo627b2o
2b2o8bo12b2o36bobo$92bo2bo26b2o621b3o14bo3bo51b2o$82b3o7bo668bo44b2o3b
2o$81bo4bo9bo13b2o3b2o628bobo61bo$80bo5bo8b2o14b5o628b5o57bo5bo$81bo8b
o20b2ob2o627b2o3b2o57b2ob2o$82b2o8b2o17b2ob2o627b2o3b2o58bobo$112b3o
694bo$82b2o8b2o715bo$81bo8bo655bo$68b2o10bo5bo8b2o650b2o$68b2o11bo4bo
9bo$82b3o7bo656bo$92bo2bo17b2o694b2o$113b2o630bo2bo60b2o$50bo3bo10b2o
678b2o$38bo9b2obobob2o7b5o$37bobo7bob2o3b2obo6bo4bo5b2o$36bo3b2o4bo2bo
5bo2bo5b3o2bo5b2o$25b2o9bo3b2o5bob2o3b2obo7bo2b2o$25b2o9bo3b2o6b2obobo
b2o9b2o$37bobo10bo3bo$38bo27b2o$65bo2b2o$48b2o14b3o2bo5b2o$41bo6b2o14b
o4bo5b2o$39b2ob2o20b5o$65b2o$38bo5bo2$38b2obob2o9$40b2o$40b2o!

Any 2c/5 gun with period 42k will work. For me, that's easier said than done. I added the x7 filter in front of the p690 gun to make a p4830 gun, making the sawtooth a catastrophe.
Best wishes to you, Scorbie
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Re: Thread For Your Useless Discoveries

Postby Scorbie » September 29th, 2014, 3:20 am

Lewis wrote:4 blocks + some junk -> twin bees shuttle variant (amongst other things):
x = 27, y = 21, rule = B3/S23
11b2ob2o$11b2ob2o2$3o21b3o$2ob3o15b3ob2o12$2ob3o15b3ob2o$3o21b3o2$11b
2ob2o$11b2ob2o!

APGsearch doesn't properly detect this, it just labels it as 'OVERSIZED'.

WOW... You must've searched a LOT to find that on soup searches... Did you tweak the source code to make symmetrical soups?
Best wishes to you, Scorbie
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Re: Thread For Your Useless Discoveries

Postby Lewis » September 29th, 2014, 1:46 pm

Scorbie wrote:WOW... You must've searched a LOT to find that on soup searches... Did you tweak the source code to make symmetrical soups?


Yep, I changed it so it generates soups with a line of symmetry through the middle. It also found this P4 oscillator which I've never seen mentioned anywhere before:
x = 16, y = 16, rule = B3/S23
3b2obo2bob2o$2bo3bo2bo3bo$o2bob6obo2bo$2bob2ob2ob2obo$2b3o2b2o2b3o$b2o
bob4obob2o$4bo2b2o2bo$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$4bo2b2o2bo$b2o
bob4obob2o$2b3o2b2o2b3o$2bob2ob2ob2obo$o2bob6obo2bo$2bo3bo2bo3bo$3b2ob
o2bob2o!


EDIT: 4 blinkers + 2 B-heptominoes -> ash includes an unusual P3 oscillator:
x = 13, y = 23, rule = B3/S23
4b3o2$b2o7b3o$2o$b2o$2bo12$2bo$b2o$2o$b2o7b3o2$4b3o!


EDIT 2: Soup generates two copies of a variation of 'Candelabra'. Sadly it forms almost immediately, and not from a particularly 'natural' mechanism...
x = 16, y = 16, rule = B3/S23
bob2o6b2obo$4b8o$2b3o6b3o$bo4b4o4bo$obo4b2o4bobo$4bobo2bobo$2ob2o2b2o
2b2ob2o$3o4b2o4b3o$3o4b2o4b3o$2ob2o2b2o2b2ob2o$4bobo2bobo$obo4b2o4bobo
$bo4b4o4bo$2b3o6b3o$4b8o$bob2o6b2obo!


Produces an interesting(ish) interaction between four pentadecathlons:
x = 16, y = 16, rule = B3/S23
2b2obob2obob2o$2o2bobo2bobo2b2o$b2o3b4o3b2o$b5ob2ob5o$2ob3ob2ob3ob2o$
3b3ob2ob3o$bo12bo$o2b4o2b4o2bo$o2b4o2b4o2bo$bo12bo$3b3ob2ob3o$2ob3ob2o
b3ob2o$b5ob2ob5o$b2o3b4o3b2o$2o2bobo2bobo2b2o$2b2obob2obob2o!
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Re: Thread For Your Useless Discoveries

Postby mniemiec » September 30th, 2014, 1:48 am

Lewis wrote:EDIT: 4 blinkers + 2 B-heptominoes -> ash includes an unusual P3 oscillator:

There is an existing synthesis of this oscillator (I believe by Jason Summers, also from a tamed soup) that requires 24 gliders. I suspect that this one will cost considerably less!
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Re: Thread For Your Useless Discoveries

Postby codeholic » September 30th, 2014, 3:34 am

Scorbie wrote:Ha! I think I made that rubegoldbergian sawtooth!

Quite impressive! I particularly like how 2c/5 spaceships toggle the back end of the c/3 spaceship. I can imagine, it's been a challenge to find it! Or was it a lucky shot?
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Re: Thread For Your Useless Discoveries

Postby Scorbie » September 30th, 2014, 10:32 am

codeholic wrote:
Scorbie wrote:Ha! I think I made that rubegoldbergian sawtooth!

Quite impressive! I particularly like how 2c/5 spaceships toggle the back end of the c/3 spaceship. I can imagine, it's been a challenge to find it! Or was it a lucky shot?

Oh, it was merely a lucky shot in many ways.
I found that through trial and error, colliding the 2c/5 streams into various c/3 spaceships. I didn't expect a clean reaction, and was planning to clean the debris by c/3 rakes. It was lucky b/c 1) It's a clean reaction 2) It's a frothing ship 3) the period is 21<->6(as good as p3 according to tedious calculations)

By the way, can anybody build a p420 2c/5 gun?
Best wishes to you, Scorbie
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Re: Thread For Your Useless Discoveries

Postby Tropylium » September 30th, 2014, 1:09 pm

Scorbie wrote:By the way, can anybody build a p420 2c/5 gun?

That would require speeding up the assembly itself a little bit. The current synthesis scheme just barely cannot handle being squeezed to p420 (the limit is p427). I haven't looked if this could be fixed just by tightening the salvos a little though or if more drastic changes would be required (e.g. using extra *WSS guns to synthesize things by octants rather than quadrants).
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Re: Thread For Your Useless Discoveries

Postby dvgrn » September 30th, 2014, 1:28 pm

Tropylium wrote:
Scorbie wrote:By the way, can anybody build a p420 2c/5 gun?

That would require speeding up the assembly itself a little bit. The current synthesis scheme just barely cannot handle being squeezed to p420 (the limit is p427).

The original 2c/5 spaceship gun was built at p416, which was the lower limit of an older recipe. See Golly's Patterns/Life/Guns/2c5-spaceship-gun-p416.rle. Any slower period is "trivial", as the saying goes -- you just need to supply a p420 edge-shooter based on the same Fx119 insertion reaction.

Given that p420 is a fairly easy period with lots of possible signal mechanisms, it's quite possible that a p420 edge-shooter can be fit inside the same bounding box as those old p416s. In that case, you can just replace all the guns without changing the locations, and the gun will still work fine. Or really it's probably easier to extract the four (or rather eight) separate glider salvos from the gun, and rebuild each shotgun separately with p420 inserters.

That's still a lot of fiddling around, though. It depends on how badly you want one of these things, I guess...!

EDIT: You can ignore my first suggestion -- a stable G-to-H converter that's as narrow as the p8 G-to-H is still not known, and 420 is not divisible by 8. A reasonably narrow-on-the-diagonal p420 edge shooter could be put together using p30N technology and maybe a few Snarks, but it's unlikely to fit in exactly the same space as those p416 guns.

Maybe someone should write a quick script to stack arbitrary edge shooters to produce shotgun salvos of this type -- unless it's been done already and I didn't notice. It's a fairly straightforward task nowadays.
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Re: Thread For Your Useless Discoveries

Postby calcyman » October 1st, 2014, 8:18 am

Ha! I think I made that rubegoldbergian sawtooth!
(Warning: It's veeery slow and painful to watch. Hyperspeed recommended.)


Here's a table of known sawteeth and their expansion factors:

Sawtooth 1846: 25
Sawtooth 1212: 21
Sawtooth 633: 11
Hacksaw: 7
Sawtooth 562: 6
Sawtooth 362: 4

Your 2c/5 sawtooth: 3451
What do you do with ill crystallographers? Take them to the mono-clinic!
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