A332929 Position where the binary expansion of n occurs for the first time in the binary expansion of Pi.

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, 17, 95, 16, 15, 13, 97, 8, 27, 45, 2, 128, 62, 146, 25, 60, 21, 395, 229, 18, 93, 209, 49, 65, 1, 78, 42, 20, 17, 105, 95, 116, 186, 16, 175, 15, 14, 13, 97, 110

Offset: 0

Author

Thomas König, Mar 02 2020

Keywords

• nonn
• base
• easy

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004601, A014777, A178707.

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

Programs

Mathematica

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 *)
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 *)

Perl

#! /usr/bin/perl
# Feed b004601.txt to this to get the binary digits of Pi.
while (<>) {
    chomp;
    (undef, $d[$n++]) = split(" ");
}
$pi = join("",@d);
$k = 0;
while (1) {
    last if ($pos = index($pi, sprintf("%b", $k++))) < 0;
    $out .= $pos +2 . ", ";
}
print $out,"\n";