A062521 -id:A062521 - cp's OEIS frontend

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

Jonathan Vos Post, Apr 25 2010

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

			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.

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

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

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

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

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

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

A063567 Smallest positive power of 4 having n in its decimal representation.

Original entry on oeis.org

5, 2, 4, 7, 1, 4, 2, 10, 7, 6, 5, 20, 25, 35, 9, 29, 2, 17, 15, 11, 28, 9, 36, 29, 5, 4, 9, 19, 24, 16, 11, 37, 38, 43, 35, 14, 8, 15, 7, 21, 6, 11, 16, 11, 9, 14, 21, 18, 10, 16, 26, 20, 30, 8, 14, 8, 4, 10, 25, 22, 22, 29, 9, 7, 3, 8, 23, 12, 14, 17, 23, 13

Offset: 0

Robert G. Wilson v, Aug 10 2001

Essentially the same as A062521.

a = {}; Do[k = 1; While[ StringPosition[ ToString[4^k], ToString[n] ] == {}, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
sp4[n_]:=Module[{k=1,idn=IntegerDigits[n]},While[SequenceCount[ IntegerDigits[ 4^k], idn] == 0, k++];k]; Array[sp4,70,0] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Mar 12 2016 *)

def a(n):
  target, k, pow4 = str(n), 1, 4
  while not target in str(pow4): k, pow4 = k+1, pow4*4
  return k
print([a(n) for n in range(72)]) # Michael S. Branicky, May 02 2021

Name edited and more terms from Michael S. Branicky, May 02 2021

cp's OEIS Frontend

A176764 Smallest power of 4 whose decimal expansion contains n.

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