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

0,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A331654 A346864 A302690 * A248779 A286030 A343684

Adjacent sequences: A030301 A030302 A030303 * A030305 A030306 A030307

Keyword

nonn,look,base

Author

Clark Kimberling

Extensions

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

Status

approved