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Search: id:A126803
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| A126803 |
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Integers which die when submitted to the rules of the Game of Life. Design of the digits is shown below. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Eric Angelini and Dean Hickerson (eric.angelini(AT)kntv.be), Feb 22 2007, Table of n, a(n) for n = 1..111
Eric Angelini, Game of Life Integers.
Dean Hickerson, Digits in Life.
Game of Life applet and description by Paul Callahan, The World of Math Online
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CROSSREFS
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Adjacent sequences: A126800 A126801 A126802 this_sequence A126804 A126805 A126806
Sequence in context: A084663 A031037 A006757 this_sequence A122990 A062372 A046031
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KEYWORD
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base,nonn
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AUTHOR
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Eric Angelini and Dean Hickerson (eric.angelini(AT)kntv.be), Feb 22 2007
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 02 2007
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