A162458 - OEIS

%I #6 Nov 03 2024 16:45:37

%S 39,12,9,7,5,5,4,4,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%T 2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N In Conway's Game of Life, the length of the shortest pattern of width n to exhibit infinite growth.

%C a(n) = 1 for n >= 39. a(1), a(5) and a(n) for n >= 39 were computed by Paul Callahan in 1998. The rest of the terms were computed in 2009.

%H <a href="http://infinitegrowth.wordpress.com/2009/06/05/n-cell-thick-patterns-1/">n-Cell Thick Patterns (1)</a> at Infinite Growth

%H <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&amp;t=78">n-Cell Thick Patterns & Infinite Growth</a> at ConwayLife.com forums

%H <a href="https://conwaylife.com/wiki/One-cell-thick_pattern">One-cell-thick pattern</a> at LifeWiki

%e a(5) = 5 because there is an infinitely-growing pattern that fits in a 5x5 box, but no infinitely-growing pattern that fits in a 5x4 box.

%K nonn

%O 1,1

%A _Nathaniel Johnston_, Jul 04 2009