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A332929
Position where the binary expansion of n occurs for the first time in the binary expansion of Pi.
2
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
COMMENTS
In contrast to this sequence, A178707 considers only the bits of pi in the fractional part (and therefore the results depend on the choice of Pi over tau = 2*Pi, which isn't the case here). - M. F. Hasler, Feb 06 2026
LINKS
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 (similar but search in the fractional part only).
Cf. A032445 (for decimal expansion rather than binary).
Sequence in context: A324081 A352522 A256262 * A361019 A157520 A325116
KEYWORD
nonn,base,easy
AUTHOR
Thomas König, Mar 02 2020
STATUS
approved