A126803 Integers that die when submitted to the rules of the Game of Life. Design of the digits is shown below.

8, 10, 11, 14, 18, 20, 31, 48, 50, 81, 83, 87, 88, 101, 118, 122, 127, 144, 148, 155, 157, 161, 174, 181, 188, 191, 199, 202, 205, 206, 208, 218, 221, 222, 228, 245, 247, 248, 274, 278, 284, 285, 295, 302, 304, 305, 308, 309, 312, 313, 315, 323, 327, 331, 342

Offset: 1

Author

Eric Angelini and Dean Hickerson, Feb 22 2007

Keywords

• base
• nonn

Comments

Here's the font that's used; a single empty column is used between adjacent digits. The same digit design was selected 39 years ago by Jonathan Vos Post.

ooo.o.ooo.ooo.o.o.ooo.ooo.ooo.ooo.ooo

o.o.o...o...o.o.o.o...o.....o.o.o.o.o

o.o.o.ooo.ooo.ooo.ooo.ooo...o.ooo.ooo

o.o.o.o.....o...o...o.o.o...o.o.o...o

ooo.o.ooo.ooo...o.ooo.ooo...o.ooo.ooo

The sequence is infinite; e.g., any number whose decimal expansion begins and ends with 14 and contains only the digits 1, 4 and 8 dies in 9 generations. It has density zero, because any number containing the digit string 14405930 emits a lightweight spaceship which can't be stopped by whatever the rest of the number produces.

Links

• Eric Angelini and Dean Hickerson, Feb 22 2007, Table of n, a(n) for n = 1..111
• Eric Angelini, Une suite pour la Vie
• E. Angelini, Une suite pour la Vie [Cached, with permission]
• Paul Callahan, Game of Life applet and description, The World of Math Online
• Dean Hickerson, Digits in Life.

Extensions

Edited by Dean Hickerson, Mar 02 2007