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

Author

Rémy Sigrist, Apr 10 2020

Keywords

• nonn
• base

Comments

Every nonnegative integer appears finitely many times in this sequence.

Links

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

Crossrefs

Cf. A047778, A161373, A161374, A333921 (decimal variant).

Programs

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)))) }

Formula

a(n) <= n with equality iff n belongs to A161374.

a(A047778(n)) = n for any n > 0.