

A333920


a(n) is the least k such that the binary representation of n appears as a substring in the concatenation of the binary representations of 0, 1, ..., k.


2



0, 1, 2, 2, 4, 3, 2, 4, 8, 5, 10, 3, 4, 3, 4, 8, 16, 9, 5, 10, 19, 11, 22, 4, 8, 5, 10, 3, 4, 7, 8, 16, 32, 17, 9, 18, 36, 5, 10, 20, 35, 19, 11, 11, 38, 22, 4, 8, 16, 9, 5, 13, 20, 11, 22, 4, 8, 5, 20, 7, 8, 15, 16, 32, 64, 33, 17, 34, 9, 35, 18, 36, 69, 37
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OFFSET

0,3


COMMENTS

Every nonnegative integer appears finitely many times in this sequence.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192


FORMULA

a(n) <= n with equality iff n belongs to A161374.
a(A047778(n)) = n for any n > 0.


PROG

(PARI) a(n, base=2) = { my (w=base^#digits(n, base), m=0); for (k=0, oo, my (d=if (k, digits(k, base), [0])); for (i=1, #d, m=(base*m+d[i])%w; if (m==n, return (k)))) }


CROSSREFS

Cf. A047778, A161373, A161374, A333921 (decimal variant).
Sequence in context: A152028 A244318 A316774 * A246815 A246836 A246953
Adjacent sequences: A333917 A333918 A333919 * A333921 A333922 A333923


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Apr 10 2020


STATUS

approved



