

A067585


Binary representation of a(n) is obtained thus: replace every digit in the binary representation of n with "1" if the sum of its neighbors is 1 and with "0" otherwise.


1



0, 0, 1, 3, 2, 0, 7, 5, 4, 6, 1, 3, 14, 12, 11, 9, 8, 10, 13, 15, 2, 0, 7, 5, 28, 30, 25, 27, 22, 20, 19, 17, 16, 18, 21, 23, 26, 24, 31, 29, 4, 6, 1, 3, 14, 12, 11, 9, 56, 58, 61, 63, 50, 48, 55, 53, 44, 46, 41, 43, 38, 36, 35, 33, 32, 34, 37, 39, 42, 40, 47, 45, 52, 54, 49, 51, 62
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OFFSET

0,4


COMMENTS

The result of one application of the following "game of life" rule to the binary representation of n: ("1" denotes a living cell, "0" a dead cell) A living cell survives, or a dead cell becomes alive, in the next generation iff the sum of its neighbors is 1 (sum = 0 or 2 implies death from isolation or overcrowding, respectively).
For n such that a(n) = n (fixed points) cf. A083713. Iteration of the mapping leads to one of these fixed points.


LINKS

Table of n, a(n) for n=0..76.
Eric Weisstein's World of Mathematics, Game of Life


EXAMPLE

6 (decimal) = 110 > 111, hence a(6) = 7; 21 (decimal) = 10101 > 00000, hence a(21) = 0. Iteration on 13 gives 13 > 12 > 14 > 11 > 3, or 1101 > 1100 > 1110 > 1011 > 11 in binary.


PROG

(PARI) {b2to10(n)=local(f, d, k); f=1; k=0; while(n>0, d=divrem(n, 10); n=d[1]; k=k+f*d[2]; f=2*f); k}
{for(n=0, 77, v=concat(0, binary(2*n)); s="0"; for(j=1, length(v)2, s=concat(s, v[j]!=v[j+2])); print1(b2to10(eval(s)), ", "))}


CROSSREFS

Cf. A083713.
Sequence in context: A319830 A309680 A010604 * A173787 A116191 A257303
Adjacent sequences: A067582 A067583 A067584 * A067586 A067587 A067588


KEYWORD

nonn,base


AUTHOR

Joseph L. Pe, Jan 31 2002


EXTENSIONS

Edited and extended by Klaus Brockhaus, Jun 14 2003


STATUS

approved



