A176771 Smallest power of 12 whose decimal expansion contains n.

20736, 1, 12, 20736, 144, 2985984, 20736, 1728, 1728, 2985984, 8916100448256, 2218611106740436992, 12, 79496847203390844133441536, 144, 5159780352, 429981696, 1728, 35831808, 61917364224, 20736, 15407021574586368

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 12 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 12^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 12 because 12^1 = 12 has "2" as a substring.
a(3) = 20736 because 12^4 = 20736 has "3" as a substring.
		

Links

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

Crossrefs

Cf. A001018, A030001, A176763, A176764-A176773.

Programs

Mathematica

A176771[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[12^++k], IntegerString[n]]]; 12^k]; Array[A176771, 50, 0] (* Paolo Xausa, Apr 04 2024 *)

Formula

a(n) = MIN{A001021(i) such that n in decimal representation is a substring of A001021(i)}.

Extensions

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

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