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.

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

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 * A356164 A246815 A246836

Adjacent sequences: A333917 A333918 A333919 * A333921 A333922 A333923

Keyword

nonn,base

Author

Rémy Sigrist, Apr 10 2020

Status

approved