A176772 Smallest power of 13 whose decimal expansion contains n.

4826809, 1, 2197, 13, 4826809, 28561, 169, 2197, 28561, 169, 10604499373, 51185893014090757, 371293, 13, 51185893014090757, 815730721, 169, 62748517, 137858491849, 2197, 1461920290375446110677, 2197, 23298085122481

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 13 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 13^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 2197 because 13^3 = 2197 has "2" as a substring.
a(3) = 13 because 13^1 = 13 has "3" as a substring.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001022, A030001, A176763, A176764-A176773.

Programs

Mathematica

A176772[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[13^++k], IntegerString[n]]]; 13^k]; Array[A176772, 50, 0] (* Paolo Xausa, Apr 04 2024 *)

Formula

a(n) = MIN{A001022(i) such that n in decimal representation is a substring of A001022(i)}.

Extensions

More terms from Sean A. Irvine and Jon E. Schoenfield, May 05 2010

a(0) prepended by Paolo Xausa, Apr 04 2024