## 15 in 15: Efficient 15-bit Synthesis Project (DONE!)

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

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Alexey_Nigin wrote:Probably useless:

`x = 35, y = 32, rule = B3/S233bo\$2bobo\$2bo2bo\$3b2o3\$3o5\$8b3o\$10bo21b2o\$8b3o20bo2bo\$32b2o9\$20bo\$20bo\$20bo\$6bo\$5bobo8b3o3b3o\$6b2o\$20bo\$20bo\$20bo!`

Moved from >15G to precisely 15G, and begging for further improvement:
`x = 103, y = 57, rule = B3/S2361bo\$62bo\$60b3o10\$93bo\$94b2o\$o92b2o\$b2o77bo\$2o79b2o\$80b2o19bo\$100bobo\$53bobo44bobo\$53b2o46bo\$54bo\$96b2o\$88bo6bo2bo\$88bo7b2o\$88bo4\$7b3o70bo\$80bo4bo\$80bo3bobo\$84bobo\$85bo\$15b3o\$17bo\$15b3o2\$87bo\$86bobo\$85bo2bo\$84bo3b2o\$85b3o2bo\$87bobo\$88bo9bo\$91b2o3b2o\$27bo63b2o4b2o\$27bo\$27bo\$13bo79b2o\$12bobo8b3o3b3o61b2o\$13b2o68b2o\$27bo55bobo\$27bo56bo\$27bo53b2o\$80bobo\$82bo!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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### Re: 15 in 15: Efficient 15-bit Synthesis Project

Later in that reaction, we get something like this to work from:

`x = 12, y = 15, rule = B3/S238b2o\$7bo2bo\$8b2o4\$o10bo\$o8bobo\$b3o4b2obo\$10bo2\$8bo\$8b2o\$9b2o\$10bo!`
Tanner Jacobi

Kazyan

Posts: 748
Joined: February 6th, 2014, 11:02 pm

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Alexey_Nigin wrote:Probably useless:

`x = 35, y = 32, rule = B3/S233bo\$2bobo\$2bo2bo\$3b2o3\$3o5\$8b3o\$10bo21b2o\$8b3o20bo2bo\$32b2o9\$20bo\$20bo\$20bo\$6bo\$5bobo8b3o3b3o\$6b2o\$20bo\$20bo\$20bo!`

Moved from >15G to precisely 15G, and begging for further improvement:
`x = 103, y = 57, rule = B3/S2361bo\$62bo\$60b3o10\$93bo\$94b2o\$o92b2o\$b2o77bo\$2o79b2o\$80b2o19bo\$100bobo\$53bobo44bobo\$53b2o46bo\$54bo\$96b2o\$88bo6bo2bo\$88bo7b2o\$88bo4\$7b3o70bo\$80bo4bo\$80bo3bobo\$84bobo\$85bo\$15b3o\$17bo\$15b3o2\$87bo\$86bobo\$85bo2bo\$84bo3b2o\$85b3o2bo\$87bobo\$88bo9bo\$91b2o3b2o\$27bo63b2o4b2o\$27bo\$27bo\$13bo79b2o\$12bobo8b3o3b3o61b2o\$13b2o68b2o\$27bo55bobo\$27bo56bo\$27bo53b2o\$80bobo\$82bo!`

Found a better cleanup:
`x = 70, y = 51, rule = B3/S23o\$b2o\$2o8\$14bo\$15b2o\$14b2o3\$67bobo\$67b2o\$68bo8\$21b3o5\$29b3o\$31bo\$29b3o10\$41bo\$41bo\$41bo\$27bo\$26bobo8b3o3b3o\$27b2o\$41bo\$41bo\$41bo!`

EDIT: Even better, all of the blinkers can be made at once:
`x = 261, y = 63, rule = B3/S232bo\$obo\$b2o4\$126bobo\$127b2o\$127bo8\$140bobo\$141b2o\$141bo2\$198bo\$196b2o33bo\$197b2o33bo\$230b3o2bo\$234bobo\$234bobo\$235bo2\$230b2o\$229bo2bo\$230b2o2\$78b3o68b3o4\$153bo4bo\$153b2ob2o\$152bobo2b2o6\$221bo35bo\$220bobo33bobo\$219bo2bo32bo2bo\$218bo3b2o30bo3b2o\$219b3o2bo30b3o2bo\$98bo70bo51bobo33bobo\$98bo70bo52bo35bo\$82bobo13bo70bo55b2o3bo\$83b2o70bo69b2o2bo\$44bo38bo10b3o3b3o51bobo8b3o3b3o55b3o\$42b2o111b2o\$43b2o38b3o12bo70bo57b2o\$83bo14bo70bo57b2o\$84bo13bo70bo47b2o\$44b2o171bobo\$43b2o173bo\$45bo169b2o\$214bobo\$216bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1707
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Alexey_Nigin wrote:Probably useless: ...

BlinkerSpawn wrote:Moved from >15G to precisely 15G, and begging for further improvement: ...

Extrementhusiast wrote:Found a better cleanup: ... EDIT: Even better, all of the blinkers can be made at once:

This also reduces the corresponding 20-bit mold to 20 (1 glider/bit), and two corresponding 21-bit oscillators to 18 and 17 (<1 glider/bit):
`x = 109, y = 77, rule = B3/S2313bo29bo29bo29bo\$12bobo27bobo27bobo27bobo\$11bobbo26bobbo26bobbo26bobbo\$10bo3boo24bo3boo24bo3boo24bo3boo\$11b3obbo8bo15b3obbo24b3obbo24b3obbo\$13bobo8boo17bobobo25bobobobb3o20bobobbo\$14bo9bobo17bobo27bobo3bo23bo\$18b3o24bo29bo5bo23boobo\$20bo58bo27bo\$19bo54boo3boo\$73bobobbobo\$20boo53bo\$20bobo\$20bo8\$33bo\$32boo\$32bobo7\$13bo29bo\$12bobo27bobo\$11bobbo26bobbo\$10bo3boo24bo3boo\$11b3obbo24b3obbo\$13bobo8bobo16bobobbo\$14bo9boo18bo3bo\$25bo22bo\$45bo\$22boo22boo\$21boo\$18bo4bo\$16boo\$17boo\$\$21b3o\$21bo\$22bo3\$20b3o\$20bo\$21bo8\$10bo\$11boo\$10boo\$14bobo\$14boo\$15bo3\$40b3o\$\$obo10bo24bo4bo\$boo9bobo23bo3bobo\$bo9bobbo23bobbobbo\$10bo3boo24bo3boo\$3boo6b3obbo24b3obbo\$4boo7bobo27bobo\$3bo10bo29bo!`
mniemiec

Posts: 929
Joined: June 1st, 2013, 12:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

AbhpzTa wrote:...
=15:
`15.446  15.447  15.485  15.487  15.516  15.598  15.653  15.751  15.786  15.83915.855  15.874  15.890  15.919  15.934  15.939  15.942  15.949  15.1024 15.103315.1034 15.1036 15.1060 15.1088`

...
>15:
`15.451  15.457  15.458  15.475  15.476  15.477  15.478  15.480  15.483  15.48615.497  15.501  15.507  15.512  15.562  15.578  15.619  15.620  15.698  15.72315.731  15.759  15.791  15.797  15.834  15.835  15.840  15.848  15.849  15.86015.868  15.918  15.923  15.947  15.960  15.983  15.986  15.1001 15.1012 15.103215.1035 15.1065`

...

My lists differ slightly from those shown:
=15:
`15.446   15.447   15.487   15.516   15.578   15.598   15.653   15.751   15.786   15.83915.855   15.876   15.890   15.891   15.919   15.934   15.939   15.942   15.949   15.102415.1033  15.1034  15.1060  15.1088`

...
>15:
`15.451   15.457   15.475   15.476   15.477   15.478   15.480   15.483   15.486   15.49715.501   15.507   15.512   15.562   15.619   15.620   15.723   15.731   15.759   15.79115.797   15.835   15.840   15.848   15.849   15.860   15.868   15.918   15.923   15.94715.960   15.983   15.986   15.1001  15.1012  15.1032  15.1065         `

From the first list are excluded 15.485(13G) 15.874(9G) 15.1036(10G) :
`x = 171, y = 145, rule = B3/S23121bo\$119b2o\$120b2o7\$106bo\$104b2o\$105b2o4\$98bo\$99bo\$97b3o\$48bo44b3o\$47bo19bo27bo11bo17b2o18b2o18b2o\$47b3o16bobo25bo11bobo16bo19bo19bo\$bo64bobo37bobo18bo2bo16bo2bo16bo2bo\$2bo47b3o14bo39bo18b5o15b5o15b5o\$3o47bo114bo\$20b2o18b2o9bo8b2o38b2o26bo13bobo3bo17b3o\$2bo17bobo17bobo17bobo37bobo24bobo13b2o2bobo18bo\$b2o18bo19bo19bo39bo26bo14bo4bo\$bobo2\$142b2o\$143b2o2b2o\$142bo4bobo\$147bo2\$87bo\$87b2o\$86bobo10\$72bo\$72b2o\$71bobo22\$12bo\$12bobo\$b2o9b2o\$2b2o41bo\$bo3bobo36bo\$5b2o37b3o\$6bo55bo19bo19bo\$22b2o18b2o17bobo17bobo17bobo\$22bo19bo18bo2bo16bo2bo16bo2bo\$23bo19bo18bobo17bobo17bobo\$24bobo17bobo14b2obobo14b2obobo14b2obob2o\$25b2o18b2o18b2o18b2o18bobo\$39b2o49bo15bo\$10bo29b2o48bobo\$9b2o28bo47b2ob2o\$9bobo31b3o40bobo\$43bo44bo\$44bo33\$3bo\$4bo\$2b3o37bo\$41bo\$41b3o5bobo\$49b2o\$50bo\$bo\$2bo15bobo21b2o7b2o\$3o15b2o23b2o5b2o\$19bo22bo9bo12b2o\$bo24b2o18b2o17bobo\$b2o24bo19bo19bo\$obo23bo19bo19bo\$26b2o18b2o18b2o\$27bo2b2o15bo2b2o15bo2b2o\$27bobobo15bobobo15bobobo\$12bobo13bo19bo19bo\$12b2o\$13bo3\$12b2o\$12bobo\$12bo!`

but included still life (15.578) of 2 list and two still life (15.876 and 15.891), which in my database belong to 15G, but I have not seen in the discussion.
From the second list are excluded 15.458(10G) 15.698(12G) 15.1035(14G):
`x = 171, y = 145, rule = B3/S2387bo\$86bo\$86b3o\$64bo\$62bobo\$63b2o\$66bo\$66bobo\$9bobo54b2o\$9b2o52bo\$10bo45bo4b2o\$57bo4b2o\$55b3o2\$96b2o18b2o18b2o\$96bo19bo19bo\$97b3o17b3o17b3o\$95bobo2bo14bobo2bo14bobo2bo\$30b3o27b3o32b2o2bobo13b2o2bobo13b2o2bobo\$100bo19bo5bo13b2o\$obo121b2o\$b2o122b2o\$bo\$124bo\$b2o29b2o28b2o59b2o\$obo29b2o28b2o59bobo\$2bo13\$5bo\$4bo\$4b3o5\$11bo3bobo\$3b2o7b2ob2o\$4b2o5b2o3bo10b2o18b2o18b2o18b2o18b2o\$3bo24bo19bo19bo19bo19bo\$28bobo17bobo17bobo17bobo5bo11bobo\$12b2o15b2o18b2o18b2o18b2o4bo13b2o\$13b2o16b2o18b2o18b2o18b2o2b3o13b2o\$12bo18bobo12bo4bobo17bobo17bobo17bo\$32bo14bo4bo19bo19bo2b3o14bo\$19bo25b3o21b3o17b3o3bo13b3o\$18b2o49bo19bo6bo12bo\$18bobo\$42bo\$40bobo6b2o\$41b2o7b2o\$44b2o3bo\$45b2o\$44bo10\$100bo\$67bo33bo\$67bobo21bo7b3o9bo\$67b2o2b3o16bobo17bobo\$71bo18bo2bo16bo2bo\$72bo18b2o18b2o3bo\$106bo9bobo\$85b3o18bo9b2o\$106bo\$108b3o\$16bo5bo85bo\$17b2o3bobo84bo4bo\$16b2o4b2o5bo84bobo\$29bobo82b2o10b2o\$29b2o95bobo\$129bo\$127b2o\$43b2ob2obo13b2ob2obo13b2ob2obo13b2ob2obo13b2obo\$42bo2b2ob2o12bo2b2ob2o12bo2b2ob2o12bo2b2ob2o12bo2b2o\$42b2o18b2o18b2o18b2o18b2o2\$114bo\$113b2o\$10b2o101bobo\$9bobo2b2o\$11bo2bobo\$14bo4\$3b2o\$2bobo\$4bo!`

One still life (15.578) to first list and one still life (15.834) appeared later published lists.

So, left to find 61 (24 +37) still life.

Bob Shemyakin
BobShemyakin

Posts: 208
Joined: June 15th, 2014, 6:24 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis

`x = 25, y = 22, rule = B3/S232\$3b2o\$3bo10b2o\$4bo9b2o\$5bobo\$6b2o6\$11bo\$10b3o\$9b2o2bo\$11bo2bo\$11b3o!`

Can anyone else...

(Here are all the 3-glider syntheses for the methulesah:
`x = 216, y = 16, rule = B3/S23b2o98b2o99bo\$obo97bobo8bo88bobo\$2bo7b3o89bo7b2o89b2o\$10bo5b2o92bobo3b2o\$11bo4bobo97bobo\$16bo99bo5\$214b2o\$213b2o\$215bo\$205b2o\$204bobo\$206bo!`

)
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 446
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Goldtiger997 wrote:I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis

I found an alternative honey-farm predecessor using 3 gliders for 11 gliders in total:

`x = 58, y = 44, rule = B3/S2327bo\$28bo\$26b3o\$55bo\$55bobo\$55b2o4\$11bo\$11bobo\$2o9b2o\$b2o\$o3bobo\$4b2o\$5bo\$31b2o\$31bo\$32bo\$33bobo\$34b2o\$48bobo\$9bo31b3o4b2o\$8b2o31bo7bo\$8bobo26b3o2bo\$39bo\$38bo\$43b3o\$43bo\$44bo12\$9b3o\$11bo\$10bo!`
chris_c

Posts: 828
Joined: June 28th, 2014, 7:15 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:... and two still life (15.876 and 15.891), which in my database belong to 15G, but I have not seen in the discussion.

I found this 9-glider synthesis of 15-876 no later than 1999-06-21:
`x = 97, y = 57, rule = B3/S2380bobo\$80boo\$35bo45bo\$36bo\$34b3o22\$20boo28boo4bo33boo\$21bo29bo4bobo32bo\$oo19bobo27bobobboo33boboboo\$boo19boo28boo5boo31b3obo\$o3boo53bobo\$4bobo52bo34boo\$4bo89boo\$\$54bobo\$54boo\$55bo\$\$54b3o\$54bo\$55bo14\$39boo\$38bobo\$40bo!`

Goldtiger997 wrote:I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis ... (Here are all the 3-glider syntheses for the methulesah: ...

chris_c wrote:I found an alternative honey-farm predecessor using 3 gliders for 11 gliders in total: ...

By making the canoe simultaneously, one of the original predecessors works, reducing this to 10:
`x = 56, y = 47, rule = B3/S23obo\$boo\$bo13\$31bobo\$31boo\$32bo6bobo\$39boo\$40bo3\$27bo\$25boo\$26boo\$\$31bo\$16bo5boo6bo\$16bobo3bobo5b3o20bo\$16boo4bo29bobo\$51bobobo\$18bo32bo3bo\$17boo33b3o\$17bobo30bobo\$50boo3\$19boo\$19bobo\$19bo5\$37boo\$36boo\$38bo!`
mniemiec

Posts: 929
Joined: June 1st, 2013, 12:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

mniemiec wrote:
Goldtiger997 wrote:I've been stuck on this highly annoying predecessor of 15.446 for a long time, and have not been to use it for a synthesis ... (Here are all the 3-glider syntheses for the methulesah: ...

chris_c wrote:I found an alternative honey-farm predecessor using 3 gliders for 11 gliders in total: ...

By making the canoe simultaneously, one of the original predecessors works, reducing this to 10:
`x = 56, y = 47, rule = B3/S23obo\$boo\$bo13\$31bobo\$31boo\$32bo6bobo\$39boo\$40bo3\$27bo\$25boo\$26boo\$\$31bo\$16bo5boo6bo\$16bobo3bobo5b3o20bo\$16boo4bo29bobo\$51bobobo\$18bo32bo3bo\$17boo33b3o\$17bobo30bobo\$50boo3\$19boo\$19bobo\$19bo5\$37boo\$36boo\$38bo!`

9 gliders: (spark + glider = block)
`x = 48, y = 39, rule = B3/S2345bo\$43b2o\$44b2o14\$16b3o\$12b2o2bo\$13b2o2bo\$6b3o3bo\$8bo32b2o\$7bo33bo2b2o\$16b3o23b2o2bo\$18bo24bobobo\$17bo25bo2bo\$22bo21b2o\$21b2o\$21bobo3\$17b2o\$17bobo9b2o\$17bo10b2o\$30bo3\$bo\$b2o\$obo!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 440
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

15.507 in 14G:
`x = 168, y = 48, rule = B3/S2318\$57bo34bo\$56bo36bo\$56b3o32b3o\$75b3o17b3o\$55bo\$12bo43bo\$13b2o33bobo3b3o5bobo\$12b2o35b2o11b2o\$49bo13bo2\$36bo8b3o8bo8b3o6b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2ob2o\$35bobo9bo7bobo7bo9bobo17bobo17bobo17bobo17bobo\$35bobo8bo8bobo8bo8bobo17bobo17bobo17bobo17bobo\$13bobo20bob2o16bob2o16bob2o16bob2o16bob2o16bob2o16bob2o\$14b2o21bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2bo\$14bo23b2o18b2o18b2o18b2o18b2o18b2o19b2o\$24bo\$15b3o5b2o104bo\$17bo5bobo104bo\$16bo111b3o\$132b2o\$131bobo3bo\$133bo3bobo\$137b2o!`

15.473 in 12G:
`x = 98, y = 40, rule = B3/S238\$25bobo40bo\$28bo40b2o\$28bo39b2o\$25bo2bo\$26b3o45bo\$72b2o\$69bo3b2o\$70b2o\$69b2o3\$30bo58bo\$28b2o20bo19bo17bobo\$29b2o18bobo8bo8bobo16bobo\$48bobo10b2o5bobo15b2obo\$47bo2bobo7b2o5bo2bobo12bobobobo\$33b3o11b2o2b2o14b2o2b2o13bo3b2o\$24bo8bo\$24b2o8bo\$23bobo\$61b3o\$63bo\$62bo3\$13bo\$13b2o\$12bobo!`

Bob Shemyakin
BobShemyakin

Posts: 208
Joined: June 15th, 2014, 6:24 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:15.507 in 14G:
`RLE`

Down to twelve gliders:
`x = 141, y = 41, rule = B3/S23111bo\$112b2o\$94bo16b2o7bo\$93bo24b2o\$93b3o19bo3b2o\$58bo27bo29b2o\$58bobo23bobo28b2o\$58b2o25b2o\$56bo\$54bobo30b2o\$55b2o29bo2bo23b2o19b2o\$61bo25b2o3bo19bo2bo18bo2bo\$17bo3bo38bobo28bobo19b2obo18b2obo\$18b2obobo36bo2bo19bo7bo2bo20bobo19bobo\$17b2o2b2o38bobo19b2o7bobo20bobo19bobo\$60b2ob2o17bobo6b2ob2o18b2ob2o17b2ob2o18\$39b2o\$38b2o\$40bo3\$bo\$b2o\$obo!`

BobShemyakin wrote:15.473 in 12G:
`RLE`

I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1707
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 15 in 15: Efficient 15-bit Synthesis Project

15.447 in 11 gliders:

`x = 91, y = 101, rule = B3/S2317bo\$bo16bo\$2bo13b3o\$3o19\$32bo\$33bo\$31b3o\$39bo\$37bobo\$38b2o8\$89bo\$88bo\$88b3o8\$66bo\$65bo\$61bo3b3o\$62b2o\$61b2o\$65b3o\$67bo\$66bo15\$81b3o\$81bo\$82bo10\$48bo\$48b2o\$47bobo17\$15b2o\$14bobo\$16bo!`
Last edited by Goldtiger997 on November 5th, 2016, 7:43 pm, edited 1 time in total.
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 446
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Goldtiger997 wrote:14.447 in 11 gliders: ...

I think you meant 15.447. By the way, thanks for all the excellent work on this project!

EDIT:
BobShemyakin wrote:15.473 in 12G: ...

You did. He improved it with a cheaper synthesis of the base still-life (12.100).
mniemiec

Posts: 929
Joined: June 1st, 2013, 12:00 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

15.457 in 11G:
`x = 213, y = 32, rule = B3/S2371bo\$72bo\$70b3o20bobo\$93b2o\$94bo\$97bobo\$67bobo27b2o\$68b2o6bo21bo\$68bo7bobo\$76b2o4\$69bo\$67bobo\$68b2o\$126b2o38b2o38b2o\$70b2o54bobo2b2o33bobo2b2o33bobo2b2o\$3bo67b2o55bo3bo35bo3bo35bo3bo\$2bo67bo39b2o15bob3o18b2o15bob3o35bob3o\$2b3o105b2o15bobo20b2o15bobo37bobo\$41b3o37b3o44bo39bo39bo\$bo145b3o\$2bo36bo39bo69bo\$3o36bo39bo68bo\$39bo39bo4\$3bo\$3b2o\$2bobo!`

BobShemyakin wrote:From the first list are excluded 15.485(13G) 15.874(9G) 15.1036(10G) :
`RLE`

but included still life (15.578) of 2 list and two still life (15.876 and 15.891), which in my database belong to 15G, but I have not seen in the discussion.
From the second list are excluded 15.458(10G) 15.698(12G) 15.1035(14G):
`RLE`

One still life (15.578) to first list and one still life (15.834) appeared later published lists.

=15
`15.487  15.516  15.578  15.598  15.653  15.751  15.786  15.839  15.855  15.89015.891  15.919  15.934  15.939  15.942  15.949  15.1024 15.1033 15.1034 15.106015.1088`
`x = 98, y = 27, rule = B3/S232o2bo8b2o5bo5bo3b2o8b2o3bo4b2o8bo10bo9b2o7b2o\$o2bobo4bobob3o3b3o2bobo3bo2bo5bobobobo3bobo3bo3b3o7bobo8bobo6bo2bo\$bobo2bo3b2o5bo5bo2bo4bobobobo5b2obo6bobobo5bo2b2o3bobo2bo6bo8b4o\$2bobobo9bo5bob2o6bobob2o7bo8b2o2bo3bo2bo2bo4b4o4bob2o11bo\$3bobo7bobo6bo11bo10bobo8bobo4b2o2bobo2bo7bobo2bo8bobo\$4bo8b2o6b2o10b2o11b2o8b2o10bo3bobo6bo2bobo6bobo\$73b2o10bo7b2o4\$2o8b2o2bo5b2ob2o8bo8b2o7bo8b2o8b2o8b2o8b2o\$o2bo6bo2bobo4bob2obo5b3o9bo6bobo7bo9bo2b2o5bo2b2o5bobobo2bo\$2b4o6b2o2bo8bo4bo5b2o4bo8bo2bo6bo3bo5bobobo5bobobo7b5o\$6bo7b2o9b2o4bo3bobo3bo10b5o5bobobo5bo3bo5bo3bo\$4b3o7bo11bo5bo2bo4bo5b2o9bo5b2o2bo9bo9bo7bo\$3bo11bo9bo7bobo5b3obobo6bobo8bobo7bobo6b3o7bobo\$3b2o9b2o9b2o7bo8b2o9b2o9b2o8b2o7bo10bo4\$o\$3o\$3bo\$2bo\$2b2o3b2o\$4bobobo\$4b2o!`

>15
`15.451  15.475  15.476  15.477  15.478  15.480  15.483  15.486  15.497  15.50115.512  15.562  15.619  15.620  15.723  15.731  15.759  15.791  15.797  15.83515.840  15.848  15.849  15.860  15.868  15.918  15.923  15.947  15.960  15.98315.986  15.1001 15.1012 15.1032 15.1065`
`x = 98, y = 37, rule = B3/S232o8b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o2bo5b2o2b2o4b2obo\$obo7bo4bo4bo2bo2bo3bo2bo2bo3bo2bo2bo3bo2bo2bo3bobobobo3bo2bobo4bo2bobo4bob4o\$2bo8b3obo5bob2o6bob2o6b3obo5b4o7b2o8b2obo5b2o13bo\$bob2obo5bobo7bo9bo11bo16bo11bob2o6b2o9b3o\$o2bob2o3bo12bobo4bobo10bo7b2o9bobo6bo11bo2bo6bo\$2o8b2o12b2o4b2o11b2o6b2o10b2o6b2o12b2o6b2o5\$2ob2obo4b2o7b2o8b2o8b2o8b2o8b2o2bo5bob2o6b2o10b2o\$bobob2o3bobo7bo2bo6bo2bo6bo9bo2bo6bo2bobo4b2obo7bo9bobo\$bo8bobob2o6b2o2b2o3b2obo7bo4bo4b2o8b2obo8b2o2b2obob2ob2o2bo\$2bo8bobo2bo6bobobo5bobobo3b2o3bobo4bob2obo6b2o9bo2bo2bob2o2bo2b5o\$3bobo6bo2bobo5bobo7bo2b2o5b2o2bo5bobob2o6bo2bo7bobo8bobo6bo\$4b2o10bo7b2o6b2o9bob2o7bo12b2o8bo10bo4bobo\$93b2o4\$bo9b2o8b2o8b2o8b2o7b2o2bo5b2o2bobo4bo9bo8bo\$obo8bobo7bobo6bo2bo6bo2bob2o3bo2bobo4bo2bob2o3bobo7bobob2o4b3o\$bobob2o7bo9bo6b2o3bo4b2o3bo5b2o2bo5b2o7bo2bo6bo3bo7bo\$3b2obo5b2o8b2o9b4o6b2o9b2o7bo8b2obobo4b3o7bo3b2o\$2bo8bo2b3o3bo2bobo7bo9bo10bo7bo11bob2o6bobo5b2o2bo\$3b3o4bobo3bo3b2o2bobo7bo10bo10bo4bo12bo10bobo6bobo\$5bo5bo13bo7b2o9b2o9b2o4b2o10b2o11bo7b2o4\$o9b2o8b2o8b2o8b2o2bo\$3o8bo9bo2b2o4bo2b2o5bo2bobo\$3bo7bob2o6bobobo5bobo8b2obo\$2b2o2bo5bobo7bo3b2o4bo2bo8bo\$3bobobo6bob2o9bo5b2obo7bobo\$3bo2bo6bobobo7bo10bo8bobo\$2b2o10bo10b2o9b2o8bo!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 440
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Nice! 15.457 30G->11G! Now the greatest cost of the 15.759 (29G).

15.480 ->14G:
`x = 140, y = 43, rule = B3/S238\$25bo\$25bobo\$25b2o\$103bo\$93bo9bobo\$13bobo75bobo9b2o\$14b2o21b2o18b2o33b2o\$8bo5bo21bobo17bobo\$9b2o26bo19bo\$8b2o44b2o\$27bobo23bobo\$27b2o11b2o13bo4b2o18b2o10bobo5b2o\$16b3o9bo11bo3b2o14bo3b2o14bo3b2o7b2o5bo3b2o13b2o3b2o\$16bo5bo19bo2bo16bo2bo16bo2bo7bo8bo2bo13bo2bo2bo\$17bo3bo19b4o16b4o16b4o16b4o16b4o\$21b3o67bo\$43b2o18b2o18b2o4bobo11b2o18b2o\$43b2o18b2o18b2o5b2o11b2o18b2o\$21b3o\$21bo70bo\$22bo69b2o\$91bobo3\$30bo\$29b2o\$29bobo!`

15.923 ->13G:
`x = 207, y = 51, rule = B3/S2315\$57bo\$58bo\$56b3o\$119bo\$120bo\$118b3o2\$121b2o\$95bobo23b2o\$95b2o\$96bo2\$19bo3bo\$20bobo97b2o28b2o18b2o18b2o\$18b3ob3o54b2ob2o36bo4b2o23bo4b2o6bo6bo4b2o13bo4b2o\$79b2ob2o38bobobo25bobobo7b2o6bobobo15bobobo\$121b3o11b2o14b3o9b2o6b3o17b3o\$92bo27bo13bobo13bo19bo19bo\$93b2obo23b2o13bo2b3o9b2o18b2o19bo\$92b2o2bobo39bo51b2o\$96b2o41bo\$43bo58bo64b2o\$42bo59bo63bobo\$42b3o57bo65bo\$170b2o\$170bobo\$42b2o126bo\$42bobo\$42bo!`

15.1012 ->11G:
`x = 77, y = 23, rule = B3/S239bo3bo30bo\$7bobob2o32b2o3bo\$2bo5b2o2b2o30b2o2b2o\$obo46b2o\$b2o22bo\$25bobo41b2o\$25b2o4bob2o11bobo2bob2o15bo2b2o\$31b2obo12b2o2b2obo15bobobo\$35b2o10bo7b2o14bo3b2o\$36bo19bo19bo\$34bo13b3o3bo19bo\$34b2o12bo5b2o18b2o\$49bo\$11b2o\$12b2o5bo\$11bo6b2o\$18bobo4\$14b3o\$16bo\$15bo!`

15.1065 ->15G:
`x = 129, y = 40, rule = B3/S239\$31bo\$31bobo\$23bo7b2o\$16bo4bobo\$17bo4b2o\$15b3o71bo\$90bo\$88b3o\$12b2o84bobo\$13b2o8bo67bobo4b2o\$12bo11bo17bo19bo19bo8b2o6bo12bo\$22b3o16bobo17bobo17bobo8bo18bobo\$37b2o3bobo12b2o3bobo17bobo27bobo\$25b2o10b2o5bo12b2o5bo19bo11bo17bo\$18b2o5bobo15bob2obo14bob2obo14bob2obo6b2o16bob2o\$18b2o5bo17bobob2o14bobob2o14bobob2o6bobo15bobo2bo\$44bo9b3o7bo19bo29bo2b2o\$56bo\$55bo\$88b2o\$89b2o3b2o\$88bo5bobo\$94bo!`

53(22 +31) still life left.
Bob Shemyakin
BobShemyakin

Posts: 208
Joined: June 15th, 2014, 6:24 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:Now the greatest cost of the 15.759 (29G).

It inspired me to try to reduce it. By completing the reduction of 15.1064 suggested here I got down to 15G:

`x = 203, y = 51, rule = B3/S2319bobo176bobo\$20b2o176b2o\$20bo178bo\$29bo\$29bobo112b2o2bo35b2o2bo11b2o\$29b2o113bo2bobo34bo2bobo10bobo\$67b3o37b3o36b2obo36b2obo10bo\$61bo39bo47b2o38b2o\$45b2o14bo23b2o14bo47bo39bo8bo\$44bo2bo13bo22bo2bo13bo49bo39bo5b2o\$45b2o38b2o63b2o38b2o5bobo\$8b2o16bo\$8bobo14b2o\$8bo16bobo\$b2o\$obo92b2o101b2o\$2bo93b2o89b2o9bobo\$95bo90bobo9bo\$188bo5\$114b3o\$114bo\$115bo\$100b2o\$100bobo\$100bo\$86b2o\$85bobo\$87bo17\$131bo\$130b2o\$130bobo!`
chris_c

Posts: 828
Joined: June 28th, 2014, 7:15 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

BobShemyakin wrote:15.1012 ->11G:
`RLE`

Unfortunately, the final step doesn't work, and we must use one more glider:
`x = 43, y = 14, rule = B3/S23bo\$2bo6bo\$3o7b2o5bo\$9b2o4b2o\$16b2o3\$35b2o\$8bo8bob2o15bo2b2o\$9bo2bo4b2obo15bobobo\$7b3o2b2o7b2o14bo3b2o\$11bobo8bo19bo\$20bo19bo\$20b2o18b2o!`

Fortunately, this still fits well under the fifteen-glider target.
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1707
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Extrementhusiast wrote:
BobShemyakin wrote:15.1012 ->11G:
`RLE`

Unfortunately, the final step doesn't work, and we must use one more glider:
`x = 43, y = 14, rule = B3/S23bo\$2bo6bo\$3o7b2o5bo\$9b2o4b2o\$16b2o3\$35b2o\$8bo8bob2o15bo2b2o\$9bo2bo4b2obo15bobobo\$7b3o2b2o7b2o14bo3b2o\$11bobo8bo19bo\$20bo19bo\$20b2o18b2o!`

Fortunately, this still fits well under the fifteen-glider target.

Thanks! 15.1012 ->12G:
`x = 87, y = 25, rule = B3/S2345bo\$46bo6bo\$9bo3bo30b3o7b2o5bo\$7bobob2o40b2o4b2o\$2bo5b2o2b2o46b2o\$obo\$b2o22bo\$25bobo51b2o\$25b2o4bob2o17bo8bob2o15bo2b2o\$31b2obo18bo2bo4b2obo15bobobo\$35b2o14b3o2b2o7b2o14bo3b2o\$36bo18bobo8bo19bo\$34bo29bo19bo\$34b2o28b2o18b2o2\$11b2o\$12b2o5bo\$11bo6b2o\$18bobo4\$14b3o\$16bo\$15bo!`

Extrementhusiast wrote:
BobShemyakin wrote:Now the greatest cost of the 15.759 (29G).

It inspired me to try to reduce it. By completing the reduction of 15.1064 suggested here I got down to 15G:

`x = 203, y = 51, rule = B3/S2319bobo176bobo\$20b2o176b2o\$20bo178bo\$29bo\$29bobo112b2o2bo35b2o2bo11b2o\$29b2o113bo2bobo34bo2bobo10bobo\$67b3o37b3o36b2obo36b2obo10bo\$61bo39bo47b2o38b2o\$45b2o14bo23b2o14bo47bo39bo8bo\$44bo2bo13bo22bo2bo13bo49bo39bo5b2o\$45b2o38b2o63b2o38b2o5bobo\$8b2o16bo\$8bobo14b2o\$8bo16bobo\$b2o\$obo92b2o101b2o\$2bo93b2o89b2o9bobo\$95bo90bobo9bo\$188bo5\$114b3o\$114bo\$115bo\$100b2o\$100bobo\$100bo\$86b2o\$85bobo\$87bo17\$131bo\$130b2o\$130bobo!`

Nice! Now the greatest cost of the 15.868 (28G).
Bob Shemyakin
BobShemyakin

Posts: 208
Joined: June 15th, 2014, 6:24 am

### Re: 15 in 15: Efficient 15-bit Synthesis Project

I have not been able to synthesise 15.451 in under 15 gliders . Does anyone know cheaper converters or a different method of construction than the one below?

`x = -75, y = -35, rule = B3/S23bbo\$3bo\$b3o\$12bo\$11bo\$11b3o\$127bo\$128bo\$3bobo120b3obbo\$4boo81bobo40bo\$4bo10bo72boo40b3o\$14bo73bo38bo\$14b3o111bo\$86boo38b3o\$17boo68boo32bobo\$17bobo12bobboo15bobboo15bobboo9bo5bobboo14boobboo5boo7boobboo18boo\$17bo13bobobbo14bobobbo14bobobbo14bobobbo14bobobbo5bo8bobobbo13boobobbo\$bo30boobo16boobo16boobo16boobo16boobo10bo5boobo14boboobo\$boo4b3o24bo19bo19bo19bo19bo11boo6bo19bo\$obo6bo15bo8bobo17bobo17bobo17bobo17bobo8bobo6bobo17bobo\$8bo15bo10boo18boo18boo18boo18boo18boo18boo\$24b3o\$35boo18boo\$35boo18boo\$10bo4b3o\$10boo5bo39b3o\$9bobo4bo40bo\$58bo9\$58bobo\$58boo\$46bo12bo\$47boo\$46boo42bo\$88bobo39bobo\$55bo33boo39boo\$54bo76bo\$54b3o14boo18boo58bo\$71boobboo14boobboo18boo11bo6boo13bobobboo\$48bobo6boo17bo19bo19bo12bo6bo14boo3bo\$49boo6bobo15bo19bo19bo11b3o5bo19bo\$49bo7bo16bo19bo19bo19bo19bo\$74bobo17bobo17bobo9b3o5bobo17bobo\$75boo18boo18boo9bo8boo18boo\$127bo14\$94bo\$85bobo5bo36bo\$88bo4b3o35bo\$40bo3bo43bo40b3o\$38boboboo41bobbo\$39boobboo17bo23b3o3bo19boo18boo\$61bobo15bobo9bobo18boo18boo\$36b3o23bo17boo10bo\$38bo41bo\$37bo3bo19bo29bo\$40bobobboo13bobobboo23bobobboo15bobboo15bobboo15bobboo\$41boo3bo14boo3bo24boo3bo14bobobbo14bobobbo14bobobbo\$45bo19bo29bo16boobo16boobo16boobo\$44bo19bo14b4o11bo19bo19bo19bo\$44bobo17bobo11bo3bo11bobo17bobo17bobo17bobo\$45boo18boo15bo12boo18boo18boo18boo\$78bobbo5boo\$86bobo\$88bo\$\$92boo\$81boo9bobo\$82boo8bo\$81bo\$90boo\$89bobo\$91bo! 15-451.rle Mark D. Niemiec's life synthesis database, Thu Feb 19 02:00:41 2015`
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 446
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 15 in 15: Efficient 15-bit Synthesis Project

They seem to be not bad.
15.835 15.983 15.860
`x = 72, y = 17, rule = B3/S2315bo24bo21bobo\$14bo24bobo20b2o\$14b3o23bo22bo\$64bo\$64bo\$58bobo\$2o56bobo\$2o59bo\$39b3o3b2o13bobo\$10bo21b2o4bo2bo3b2o13bobo\$9bobo21b2o3b3o20bo\$2b2o6b2o21b2o\$2bo2bo27b2o35bo\$32b3o34bobo\$3bobo19b2o2b2ob2o35bobo\$5bo19b2ob3ob2o36bo\$3o!`
Last edited by yootaa on November 6th, 2016, 8:36 am, edited 1 time in total.

yootaa

Posts: 35
Joined: May 26th, 2016, 1:08 am
Location: Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

I wrote:I have not been able to synthesise 15.451 in under 15 gliders . Does anyone know cheaper converters or a different method of construction than the one below?

`x = -75, y = -35, rule = B3/S23bbo\$3bo\$b3o\$12bo\$11bo\$11b3o\$127bo\$128bo\$3bobo120b3obbo\$4boo81bobo40bo\$4bo10bo72boo40b3o\$14bo73bo38bo\$14b3o111bo\$86boo38b3o\$17boo68boo32bobo\$17bobo12bobboo15bobboo15bobboo9bo5bobboo14boobboo5boo7boobboo18boo\$17bo13bobobbo14bobobbo14bobobbo14bobobbo14bobobbo5bo8bobobbo13boobobbo\$bo30boobo16boobo16boobo16boobo16boobo10bo5boobo14boboobo\$boo4b3o24bo19bo19bo19bo19bo11boo6bo19bo\$obo6bo15bo8bobo17bobo17bobo17bobo17bobo8bobo6bobo17bobo\$8bo15bo10boo18boo18boo18boo18boo18boo18boo\$24b3o\$35boo18boo\$35boo18boo\$10bo4b3o\$10boo5bo39b3o\$9bobo4bo40bo\$58bo9\$58bobo\$58boo\$46bo12bo\$47boo\$46boo42bo\$88bobo39bobo\$55bo33boo39boo\$54bo76bo\$54b3o14boo18boo58bo\$71boobboo14boobboo18boo11bo6boo13bobobboo\$48bobo6boo17bo19bo19bo12bo6bo14boo3bo\$49boo6bobo15bo19bo19bo11b3o5bo19bo\$49bo7bo16bo19bo19bo19bo19bo\$74bobo17bobo17bobo9b3o5bobo17bobo\$75boo18boo18boo9bo8boo18boo\$127bo14\$94bo\$85bobo5bo36bo\$88bo4b3o35bo\$40bo3bo43bo40b3o\$38boboboo41bobbo\$39boobboo17bo23b3o3bo19boo18boo\$61bobo15bobo9bobo18boo18boo\$36b3o23bo17boo10bo\$38bo41bo\$37bo3bo19bo29bo\$40bobobboo13bobobboo23bobobboo15bobboo15bobboo15bobboo\$41boo3bo14boo3bo24boo3bo14bobobbo14bobobbo14bobobbo\$45bo19bo29bo16boobo16boobo16boobo\$44bo19bo14b4o11bo19bo19bo19bo\$44bobo17bobo11bo3bo11bobo17bobo17bobo17bobo\$45boo18boo15bo12boo18boo18boo18boo\$78bobbo5boo\$86bobo\$88bo\$\$92boo\$81boo9bobo\$82boo8bo\$81bo\$90boo\$89bobo\$91bo! 15-451.rle Mark D. Niemiec's life synthesis database, Thu Feb 19 02:00:41 2015`

The equivalent with a python has 1 soup on catalogue (the original had none). Here are two reductions:

`x = 60, y = 25, rule = B3/S232b3o2\$o5bo45b3o\$o5bo45bobo\$o5bo45b3o2\$2b3o2\$2bo\$2bo48bo\$2b2o46bobo\$2b3o3b2o39bo2bo5b2o\$2b2o4b2o40b2o6b2o2\$4bo42b2o\$46b2o\$5bo34b2o5bobo\$3b3o33bo2bo5b2o\$40b2o12bo\$53b3o\$52b5o\$51b2o3b2o\$52b5o\$53b3o\$54bo!`

If anyone can use either of those to make a synthesis in 11 gliders or less, we can use the following converter to synthesise 15.451 in under 15 gliders.

`x = 16, y = 12, rule = B3/S234bo\$5bo\$3b3o3\$8b2o4b2o\$2bo5bobobo2bo\$obo8b2obo\$b2o10bo\$4b2o7bobo\$5b2o7b2o\$4bo!`

This is quite a hard one!
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 446
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 15 in 15: Efficient 15-bit Synthesis Project

yootaa wrote:They seem to be not bad.
15.835 15.938 15.860

That last one (15.860) is just part of loafer along with a traffic light and beehive:
`x = 29, y = 32, rule = B3/S232bo\$obo\$b2o2\$26bo\$26bobo\$26b2o8\$11bo\$11bobo\$11b2o2\$10bo\$8bobo\$5bo3b2o\$5b2o\$4bobo6\$24bo\$23bobo\$23bobo\$24bo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1265
Joined: July 9th, 2009, 2:44 pm

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Sokwe wrote:
yootaa wrote:They seem to be not bad.
15.835 15.938 15.860

That last one (15.860) is just part of loafer along with a traffic light and beehive:
`x = 29, y = 32, rule = B3/S232bo\$obo\$b2o2\$26bo\$26bobo\$26b2o8\$11bo\$11bobo\$11b2o2\$10bo\$8bobo\$5bo3b2o\$5b2o\$4bobo6\$24bo\$23bobo\$23bobo\$24bo!`

Thank you!
15.860 in 9G:
`x = 48, y = 60, rule = B3/S232bo\$obo\$b2o4\$11bo\$9bobo\$10b2o2\$35bo\$35bobo\$35b2o8\$20bo\$20bobo\$20b2o2\$19bo\$17bobo\$14bo3b2o\$14b2o\$13bobo5\$34bo\$34bobo\$34b2o2\$37b2o\$37bobo\$37bo18\$46b2o\$45b2o\$47bo!`

yootaa

Posts: 35
Joined: May 26th, 2016, 1:08 am
Location: Japan

### Re: 15 in 15: Efficient 15-bit Synthesis Project

Goldtiger997 wrote:If anyone can use either of those to make a synthesis in 11 gliders or less, we can use the following converter to synthesise 15.451 in under 15 gliders.

15.451 in 14:
`x = 231, y = 25, rule = B3/S232bo\$obo\$b2o5\$38b2o28b2o135bo\$38b2o28b2o34b2o28b2o28b2o28b2o7b2o19b2o\$104bobo27bobo27bobo27bobo7b2o18bobo\$11bo94bo29bo29bo29bo10b2o17bo\$10bo22b2o21bo6b2o12bo27bob2o26bob2o26bob2o26bob2o8bobo15bob2obo\$10b3o19bo2bo21b2o3bo2bo11bobo24bo2bobobo22bo2bobobo22bo2bobobo22bo2bobobo5bo16bo2bob2o\$7b2o24b2o21b2o5b2o12b2o2b2o21b2o4b2o22b2o4b2o22b2o4b2o22b2o4b2o22b2o\$6bobo30b3o27b3o9bobo\$8bo72bo26bo29bo\$107bobo27bobo64b3o\$65b2o40bobo27bobo64bo\$19bo40b2o2bobo41bo29bo66bo\$18b2o41b2o3bo\$18bobo39bo77b2o\$138bobo\$66bo71bo\$65b2o\$65bobo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1265
Joined: July 9th, 2009, 2:44 pm

### Re: 15 in 15: Efficient 15-bit Synthesis Project

yootaa wrote:They seem to be not bad.
15.835 15.983 15.860
`x = 72, y = 17, rule = B3/S2315bo24bo21bobo\$14bo24bobo20b2o\$14b3o23bo22bo\$64bo\$64bo\$58bobo\$2o56bobo\$2o59bo\$39b3o3b2o13bobo\$10bo21b2o4bo2bo3b2o13bobo\$9bobo21b2o3b3o20bo\$2b2o6b2o21b2o\$2bo2bo27b2o35bo\$32b3o34bobo\$3bobo19b2o2b2ob2o35bobo\$5bo19b2ob3ob2o36bo\$3o!`

15.983 in 9G:
`x = 61, y = 68, rule = B3/S2359bo\$58bo\$58b3o4\$55bo\$54bo\$54b3o6\$39bo\$38bo\$15bo22b3o\$13bobo\$14b2o18\$20bo16b2o\$21b2o14bobo\$20b2o3bo11bo\$23b2o\$24b2o32bo\$57b2o\$57bobo23\$3o\$2bo\$bo!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

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Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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