A333921 a(n) is the least k such that the decimal representation of n appears as a substring in the concatenation of 0, 1, ..., k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 13, 14, 15, 16, 17, 18, 19, 20, 13, 22, 3, 24, 25, 26, 27, 28, 29, 30, 14, 24, 33, 4, 35, 36, 37, 38, 39, 40, 15, 25, 35, 44, 5, 46, 47, 48, 49, 50, 16, 26, 36, 46, 55, 6, 57, 58, 59, 60, 17, 27, 37, 47, 57, 66, 7, 68

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..10000

Crossrefs

Cf. A007908, A116700, A131881, A333920 (binary variant).

Programs

PARI

a(n, base=10) = { 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 = 0 or n belongs to A131881.

a(A007908(n)) = n for any n > 0.