A176770 Smallest power of 11 whose decimal expansion contains n.

161051, 1, 121, 1331, 14641, 161051, 14641, 1771561, 19487171, 19487171, 161051, 11, 121, 1331, 14641, 1771561, 161051, 1771561, 9849732675807611094711841, 19487171, 672749994932560009201, 121, 34522712143931, 2357947691, 25937424601

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 11 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 11^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 121 because 11^2 = 121 has "2" as a substring.
a(3) = 1331 because 11^3 = 1331 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

A176770[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[11^++k], IntegerString[n]]]; 11^k]; Array[A176770, 50, 0] (* Paolo Xausa, Apr 04 2024 *)

Formula

a(n) = MIN{A001020(i) such that n in decimal representation is a substring of A001020(i)}.

Extensions

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

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