A333921 -id:A333921 - cp's OEIS frontend

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

Rémy Sigrist, Apr 10 2020

Every nonnegative integer appears finitely many times in this sequence.

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

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

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)))) }

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

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

A341537 a(n) is the number of digits from the end of the concatenation of all previous terms where n last appears. If n has not previously appeared then a(n) = n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 2, 14, 15, 16, 17, 18, 19, 20, 15, 22, 33, 24, 25, 26, 27, 28, 29, 30, 31, 17, 20, 54, 35, 36, 37, 38, 39, 40, 53, 35, 17, 44, 75, 46, 5, 48, 49, 50, 16, 52, 23, 13, 55, 95, 57, 58, 7, 60, 87, 69, 51, 64, 26, 66, 115, 68, 15, 70, 106, 79, 71, 61, 36

Offset: 0

Scott R. Shannon, Feb 14 2021

			a(9) = 9 as the concatenation of all previous terms is "012345678" which does not include 9, so a(9) = 9.
a(12) = 13 as the concatenation of all previous terms is "01234567891011" which includes "12" as a substring, starting 13 digits from the end of the concatenation.
a(13) = 2 as the concatenation of all previous terms is "0123456789101113" which includes "13" as a substring, starting 2 digits from the end of the concatenation.

Scott R. Shannon, Image of the terms for n=0..500000.

Cf. A333921, A337227, A007908, A116700, A131881.

cp's OEIS Frontend

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.

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