A327984 Positions of ones in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

0, 1, 3, 4, 5, 8, 9, 13, 15, 16, 19, 22, 23, 24, 26, 28, 29, 30, 33, 34, 35, 37, 39, 41, 42, 47, 48, 51, 53, 55, 56, 58, 60, 62, 63, 64, 65, 66, 67, 72, 73, 74, 75, 79, 81, 83, 84, 85, 91, 94, 96, 97, 101, 102, 103, 107, 108, 110, 111, 113, 114, 116, 124, 128, 129, 130, 131, 132, 134, 135, 136, 138, 141, 142, 143, 147

Offset: 1

Author

Antti Karttunen, Oct 03 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A051023 (characteristic function), A110240, A269160.

Cf. A327981 (first differences), A327982 (a left inverse), A327985 (complement).

Programs

Mathematica

A327984list[upto_]:=Flatten[Position[CellularAutomaton[30,{{1},0},{upto,{{0}}}],1]]-1;A327984list[200] (* Paolo Xausa, Jun 28 2023 *)

PARI

A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
A110240(n) = if(!n,1,A269160(A110240(n-1)));
A051023(n) = ((A110240(n)>>n)%2);
isA327984(n) = A051023(n);

PARI

A327984write(up_to) = { my(s=1, n=0, k=0); while(k>n)%2, k++; write("b327984.txt", k, " ", n)); s = A269160(s); n++); (n); }; \\ For fast creation of b-files.

Formula

For all n >= 1, A327982(a(n)) = n.