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

Author

Antti Karttunen, Feb 22 2016

Keywords

• nonn

Examples

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

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

Crossrefs

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

Cf. A267365 (iterates starting from 1).

Cf. A269174.

Programs

C

#include 
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 */

Mathematica

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

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

Scheme

(define (A269173 n) (A003986bi (A048724 n) (A048725 n)))

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).]