A267357 Decimal representation of the n-th iteration of the "Rule 124" elementary cellular automaton starting with a single ON (black) cell.

1, 3, 7, 11, 31, 35, 103, 235, 383, 899, 1415, 3979, 4511, 13219, 30183, 48747, 116479, 184067, 512775, 587531, 1653535, 3890979, 6284135, 14706667, 23128191, 65108099, 73636231, 216382347, 493870495, 804319139, 1882288615, 2960372331, 8333424383, 9428680451

Offset

0,2

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

a(0) = 1, and for n > 0, a(n) = A269174(a(n-1)). - Antti Karttunen, Apr 16 2026

Mathematica

rule=124; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

Prog

(PARI)
A269174(n) = bitand(bitor(n, n<<1), bitor(bitxor(n, n<<1), bitxor(n, n<<2)));
A267357(n) = if(!n, 1, A269174(A267357(n-1))); \\ Antti Karttunen, Apr 16 2026

Crossrefs

Iterates of map n -> A269174(n) starting from n=1.

Cf. A267356 (same terms shown in binary), A267355 (in a triangle form).

Sequence in context: A238673 A318263 A213740 * A152084 A389481 A274134

Adjacent sequences: A267354 A267355 A267356 * A267358 A267359 A267360

Keyword

nonn,easy

Author

Robert Price, Jan 13 2016

Status

approved