A269174 Formula for Wolfram's Rule 124 cellular automaton: a(n) = (n OR 2n) AND ((n XOR 2n) OR (n XOR 4n)).

0, 3, 6, 7, 12, 15, 14, 11, 24, 27, 30, 31, 28, 31, 22, 19, 48, 51, 54, 55, 60, 63, 62, 59, 56, 59, 62, 63, 44, 47, 38, 35, 96, 99, 102, 103, 108, 111, 110, 107, 120, 123, 126, 127, 124, 127, 118, 115, 112, 115, 118, 119, 124, 127, 126, 123, 88, 91, 94, 95, 76, 79, 70, 67, 192, 195, 198, 199, 204, 207, 206, 203, 216

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..32767

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

a(n) = A163617(n) AND A269173(n).

a(n) = A163617(n) AND (A048724(n) OR A048725(n)).

a(n) = (n OR 2n) AND ((n XOR 2n) OR (n XOR 4n)).

Other identities. For all n >= 0:

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

a(n) = A057889(A161903(A057889(n))). [Rule 124 is the mirror image of rule 110.]

G.f.: (-3*x^3 - 2*x^2 - 3*x)/(x^4 - 1) + Sum_{k>=1}((2^(k + 1)*x^(2^k) - 2^(k + 1)*x^(14*2^(k - 2)))/((x^(2^(k + 2)) - 1)*(x - 1))). - Miles Wilson, Jan 25 2025

Mathematica

a[n_] := BitAnd[BitOr[n, 2n], BitOr[BitXor[n, 2n], BitXor[n, 4n]]];
a /@ Range[0, 100] (* Jean-François Alcover, Feb 23 2020 *)

Prog

(Scheme) (define (A269174 n) (A004198bi (A163617 n) (A003986bi (A048724 n) (A048725 n))))
(Python) def a(n): return (n|2*n)&((n^(2*n))|(n^(4*n))) # Indranil Ghosh, Apr 19 2017
(Go)
package main
import "fmt"
func main() {
    for n:=0; n<=100; n++{
    fmt.Println((n|2*n)&((n^(2*n))|(n^(4*n))))}
} // Indranil Ghosh, Apr 19 2017

Crossrefs

Cf. A003986, A003987, A004198, A048724, A048725, A057889, A269173, A161903.

Cf. A269175.

Cf. A269176 (numbers not present in this sequence).

Cf. A269177 (same sequence sorted into ascending order, duplicates removed).

Cf. A269178 (numbers that occur only once).

Cf. A267357 (iterates from 1 onward).

Sequence in context: A226228 A365422 A335431 * A161903 A163617 A189634

Adjacent sequences: A269171 A269172 A269173 * A269175 A269176 A269177

Keyword

nonn

Author

Antti Karttunen, Feb 22 2016

Status

approved