A176764 Smallest power of 4 whose decimal expansion contains n.

1024, 1, 256, 16384, 4, 256, 16, 1048576, 16384, 4096, 1024, 1099511627776, 1125899906842624, 1180591620717411303424, 262144, 288230376151711744, 16, 17179869184, 1073741824, 4194304, 72057594037927936, 262144, 4722366482869645213696

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 4 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 4^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 256 because 4^4 = 256 has "2" as a substring.
a(3) = 16384 because 4^7 = 16384 has "3" as a substring.
		

Links

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

Crossrefs

Cf. A000302, A030001, A176763, A176765-A176773.

Programs

Mathematica

A176764[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[4^++k], IntegerString[n]]]; 4^k]; Array[A176764, 50, 0] (* Paolo Xausa, Apr 03 2024 *)

Formula

a(n) = MIN{A000302(i) such that n in decimal representation is a substring of A000302(i)}.

a(n) = 4^A062521(n). - Michel Marcus, Sep 30 2014

Extensions

Corrected and extended by Sean A. Irvine and Jon E. Schoenfield, May 05 2010

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