A176765 Smallest power of 5 whose decimal expansion contains n.

390625, 1, 25, 3125, 48828125, 5, 625, 78125, 78125, 390625, 6103515625, 11920928955078125, 125, 931322574615478515625, 244140625, 15625, 95367431640625, 30517578125, 2384185791015625, 1953125, 1220703125, 116415321826934814453125

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 5 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 5^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 25 because 5^2 = 25 has "2" as a substring.
a(3) = 3125 because 5^5 = 3125 has "3" as a substring.
		

Links

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

Crossrefs

Cf. A000351, A030001, A176763, A176764-A176773.

Programs

Mathematica

A176765[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[5^++k], IntegerString[n]]]; 5^k]; Array[A176765, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

Formula

a(n) = MIN{A000351(i) such that n in decimal representation is a substring of A000351(i)}.

a(n) = 5^A062522(n). - Michel Marcus, Sep 30 2014

Extensions

Corrected comment by Sean A. Irvine, May 05 2010

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

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