A176766 Smallest power of 6 whose decimal expansion contains n.

10077696, 1, 216, 36, 46656, 46656, 6, 7776, 2176782336, 1296, 10077696, 2821109907456, 1296, 13060694016, 6140942214464815497216, 101559956668416, 216, 60466176, 470184984576, 21936950640377856, 170581728179578208256, 216

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 6 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 6^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 216 because 6^3 = 216 has "2" as a substring.
a(3) = 36 because 6^2 = 36 has "3" as a substring.
		

Links

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

Crossrefs

Cf. A000400, A030001, A176763, A176764-A176773.

Programs

Mathematica

A176766[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[6^++k], IntegerString[n]]]; 6^k]; Array[A176766, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

Formula

a(n) = MIN{A000400(i) such that n in decimal representation is a substring of A000400(i)}.

a(n) = 6^A062523(n). - Michel Marcus, Sep 30 2014

Extensions

Corrected and extended by Sean A. Irvine and Jon E. Schoenfield, May 05 2010

a(0) prepended by Paolo Xausa, Apr 03 2024