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

0,1

Links

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

Example

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

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 *)

Prog

(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";

Crossrefs

Cf. A004601, A014777, A178707.

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

Sequence in context: A324081 A352522 A256262 * A361019 A157520 A325116

Adjacent sequences: A332926 A332927 A332928 * A332930 A332931 A332932

Keyword

nonn,base,easy

Author

Thomas König, Mar 02 2020

Status

approved