A059711 Smallest base in which n is a repdigit.

2, 2, 3, 2, 3, 4, 5, 2, 3, 8, 4, 10, 5, 3, 6, 2, 7, 16, 5, 18, 9, 4, 10, 22, 5, 24, 3, 8, 6, 28, 9, 2, 7, 10, 16, 6, 8, 36, 18, 12, 3, 40, 4, 6, 10, 8, 22, 46, 7, 48, 9, 16, 12, 52, 8, 10, 13, 7, 28, 58, 9, 60, 5, 2, 15, 12, 10, 66, 16, 22, 9, 70, 11, 8, 36, 14, 18, 10, 12, 78, 3, 26, 40, 82, 11, 4

Offset: 0

Author

Erich Friedman, Feb 19 2001

Keywords

• base
• easy
• nonn

Comments

Numbers n such that a(n) < n - 1 correspond to Brazilian numbers (A125134); conversely, positive numbers n such that a(n) >= n - 1 correspond to A220570. - Rémy Sigrist, Apr 04 2018

Examples

			a(13) = 3 since 13 in base 3 is 111.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A010785, A125134, A048328, A048329, A048330, A048331, A048332, A048333, A048334, A048335, A048336, A048337, A048338, A048339, A048340, A220570.

Programs

PARI

a(n) = for (b=2, oo, if (#Set(digits(n, b))<=1, return (b))) \\ Rémy Sigrist, Apr 04 2018

Formula

From Rémy Sigrist, Apr 04 2018: (Start)

a(n) <= n - 1 for any n >= 3.

a(2^n-1) = 2 for any n >= 0.

a(A048328(n)) <= 3 for any n >= 0.

a(A048329(n)) <= 4 for any n >= 0.

a(A048330(n)) <= 5 for any n >= 0.

a(A048331(n)) <= 6 for any n >= 0.

a(A048332(n)) <= 7 for any n >= 0.

a(A048333(n)) <= 8 for any n >= 0.

a(A048334(n)) <= 9 for any n >= 0.

a(A010785(n)) <= 10 for any n >= 0.

a(A048335(n)) <= 11 for any n >= 0.

a(A048336(n)) <= 12 for any n >= 0.

a(A048337(n)) <= 13 for any n >= 0.

a(A048338(n)) <= 14 for any n >= 0.

a(A048339(n)) <= 15 for any n >= 0.

a(A048340(n)) <= 16 for any n >= 0.

(End)

Extensions

Example clarified by Harvey P. Dale, Oct 11 2015

Terms a(0) = 2, a(1) = 2 and a(2) = 3 prepended by Rémy Sigrist, Apr 04 2018