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 A269173 Formula for Wolfram's Rule 126 cellular automaton: a(n) = (n XOR 2n) OR (n XOR 4n). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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(0, 101)] # Indranil Ghosh, Apr 02 2017 (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 */ 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

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Last modified April 11 02:02 EDT 2021. Contains 342886 sequences. (Running on oeis4.)