A030304 Least k such that the base-2 representation of n begins at s(k), where s=A030190 (or equally A030302).

0, 1, 2, 1, 6, 2, 1, 4, 18, 6, 26, 2, 5, 1, 4, 15, 50, 18, 6, 22, 63, 26, 77, 2, 17, 5, 25, 1, 4, 11, 15, 46, 130, 50, 18, 55, 154, 6, 22, 65, 146, 63, 26, 28, 163, 77, 2, 13, 49, 17, 5, 34, 69, 25, 79, 1, 16, 4, 68, 11, 15, 41, 46, 125, 322, 130, 50

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• look
• base

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A030190, A030302, A031297 (decimal variant), A055143.

Programs

Mathematica

nmax = 100;
s = Table[IntegerDigits[n, 2], {n, 0, nmax}] // Flatten;
a[n_] := SequencePosition[s, IntegerDigits[n, 2], 1][[1, 1]] - 1;
a /@ Range[0, nmax] (* Jean-François Alcover, Feb 21 2021 *)

Perl

$bb = ""; foreach $n (0..66) { print index($bb .= $b = sprintf("%b", $n), $b), ", "; } # Rémy Sigrist, Aug 19 2020

Python

from itertools import count, islice
def agen():
    k, chap = 0, "0"
    for n in count(0):
        target = bin(n)[2:]
        while chap.find(target) == -1: k += 1; chap += bin(k)[2:]
        yield chap.find(target)
print(list(islice(agen(), 70))) # Michael S. Branicky, Oct 06 2022

Formula

a(n) = 1 iff n belongs to A055143. - Rémy Sigrist, Feb 20 2021

Extensions

Minor edits by N. J. A. Sloane, Dec 16 2017