A176769 Smallest power of 9 whose decimal expansion contains n.

59049, 1, 729, 531441, 59049, 6561, 6561, 729, 81, 9, 31381059609, 205891132094649, 150094635296999121, 31381059609, 531441, 150094635296999121, 16677181699666569, 1350851717672992089, 2541865828329, 8862938119652501095929

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 9 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 9^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 729 because 9^3 = 729 has "2" as a substring.
a(3) = 531441 because 9^6 = 531441 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

A176769[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[9^++k], IntegerString[n]]]; 9^k]; Array[A176769, 50, 0] (* Paolo Xausa, Apr 04 2024 *)

Formula

a(n) = MIN{A001019(i) such that n in decimal representation is a substring of A001019(i)}.

a(n) = 9^A062526(n). - Michel Marcus, Sep 30 2014

Extensions

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

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