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Position where the binary expansion of n occurs for the first time in the binary expansion of Pi.
1

%I #19 Sep 18 2021 18:55:21

%S 3,1,2,1,2,18,1,13,8,2,21,18,1,17,16,13,8,27,2,62,25,21,18,93,49,1,20,

%T 17,95,16,15,13,97,8,27,45,2,128,62,146,25,60,21,395,229,18,93,209,49,

%U 65,1,78,42,20,17,105,95,116,186,16,175,15,14,13,97,110

%N Position where the binary expansion of n occurs for the first time in the binary expansion of Pi.

%H Harvey P. Dale, <a href="/A332929/b332929.txt">Table of n, a(n) for n = 0..1000</a>

%e In binary, Pi = 11.00100100.... The bitstring 10 (for 2) occurs at position 2, so a(2) = 2.

%t p = RealDigits[Pi,2,500][[1]]; L = {}; Do[t = SequencePosition[p, IntegerDigits[n, 2], 1]; If[t == {}, Break[], AppendTo[L, t[[1, 1]]]], {n, 0, 65}]; L (* _Giovanni Resta_, Mar 16 2020 *)

%t Module[{nn=500,bp},bp=RealDigits[Pi,2,nn][[1]];Table[ SequencePosition[ bp,IntegerDigits[n,2],1][[All,1]],{n,0,70}]]//Flatten (* _Harvey P. Dale_, Sep 18 2021 *)

%o (Perl)

%o #! /usr/bin/perl

%o # Feed b004601.txt to this to get the binary digits of Pi.

%o while (<>) {

%o chomp;

%o (undef, $d[$n++]) = split(" ");

%o }

%o $pi = join("",@d);

%o $k = 0;

%o while (1) {

%o last if ($pos = index($pi, sprintf("%b", $k++))) < 0;

%o $out .= $pos +2 . ", ";

%o }

%o print $out,"\n";

%Y Cf. A004601, A014777, A178707.

%Y Cf. A032445 (for decimal expansion rather than binary).

%K nonn,base,easy

%O 0,1

%A _Thomas König_, Mar 02 2020