A269173 Formula for Wolfram's Rule 126 cellular automaton: a(n) = (n XOR 2n) OR (n XOR 4n).

0, 7, 14, 15, 28, 31, 30, 27, 56, 63, 62, 63, 60, 63, 54, 51, 112, 119, 126, 127, 124, 127, 126, 123, 120, 127, 126, 127, 108, 111, 102, 99, 224, 231, 238, 239, 252, 255, 254, 251, 248, 255, 254, 255, 252, 255, 246, 243, 240, 247, 254, 255, 252, 255, 254, 251, 216, 223, 222, 223, 204, 207, 198, 195, 448, 455, 462

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Eric Weisstein's World of Mathematics, Rule 126

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

a(n) = A048724(n) OR A048725(n) = (n XOR 2n) OR (n XOR 4n), where OR is a bitwise-or (A003986) and XOR is A003987.

Other identities. For all n >= 0:

a(2*n) = 2*a(n).

a(n) = A057889(a(A057889(n))). [Rule 126 is amphichiral (symmetric).]

Example

a(4) = (4 XOR 2*4) OR (4 XOR 4*4) = 12 OR 20 = 28. - Indranil Ghosh, Apr 02 2017

Mathematica

Table[BitOr[BitXor[n, 2n], BitXor[n, 4n]], {n, 0, 100}] (* Indranil Ghosh, Apr 02 2017 *)

Prog

(Scheme) (define (A269173 n) (A003986bi (A048724 n) (A048725 n)))
(PARI) for(n=0, 100, print1(bitor(bitxor(n, 2*n), bitxor(n, 4*n)), ", ")) \\ Indranil Ghosh, Apr 02 2017
(Python) print([(n^(2*n))|(n^(4*n)) for n in range(101)]) # Indranil Ghosh, Apr 02 2017
(C)
#include <stdio.h>
int main()
{
    int n;
    for(n=0; n<=100; n++){
        printf("%d, ", (n^(2*n))|(n^(4*n)));
    }
    return 0;
} /* Indranil Ghosh, Apr 02 2017 */

Crossrefs

Cf. A003986, A003987, A048724, A048725, A057889.

Cf. A267365 (iterates starting from 1).

Cf. A269174.

Sequence in context: A173024 A115770 A086779 * A167197 A336797 A100599

Adjacent sequences: A269170 A269171 A269172 * A269174 A269175 A269176

Keyword

nonn

Author

Antti Karttunen, Feb 22 2016

Status

approved