A176767 Smallest power of 7 whose decimal expansion contains n.

2401, 1, 2401, 343, 49, 823543, 16807, 7, 16807, 49, 96889010407, 117649, 13841287201, 13841287201, 11398895185373143, 4747561509943, 16807, 117649, 11398895185373143, 1977326743, 13841287201, 3909821048582988049

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 7 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 7^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 2401 because 7^4 = 2401 has "2" as a substring.
a(3) = 343 because 7^3 = 343 has "3" as a substring.
		

Links

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

Crossrefs

Cf. A000420, A030001, A176763, A176764-A176773.

Programs

Mathematica

A176767[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[7^++k], IntegerString[n]]]; 7^k]; Array[A176767, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

Formula

a(n) = MIN{A000420(i) such that n in decimal representation is a substring of A000420(i)}.

a(n) = 7^A062524(n). - Michel Marcus, Sep 30 2014

Extensions

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

Extended to a(0) by M. F. Hasler, Oct 03 2014