A327984 - OEIS

%I #12 Jun 29 2023 02:30:08

%S 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,

%T 47,48,51,53,55,56,58,60,62,63,64,65,66,67,72,73,74,75,79,81,83,84,85,

%U 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

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

%H Antti Karttunen, <a href="/A327984/b327984.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

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

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

%o (PARI)

%o A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.

%o A110240(n) = if(!n,1,A269160(A110240(n-1)));

%o A051023(n) = ((A110240(n)>>n)%2);

%o isA327984(n) = A051023(n);

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

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

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

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 03 2019