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

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

Author

Robert G. Wilson v, Aug 10 2001

Keywords

• base
• nonn

Crossrefs

Essentially the same as A062521.

Programs

Mathematica

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 *)

Python

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

Extensions

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