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Smallest positive power of 4 having n in its decimal representation.
2

%I #14 May 02 2021 11:11:26

%S 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,

%T 24,16,11,37,38,43,35,14,8,15,7,21,6,11,16,11,9,14,21,18,10,16,26,20,

%U 30,8,14,8,4,10,25,22,22,29,9,7,3,8,23,12,14,17,23,13

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

%t a = {}; Do[k = 1; While[ StringPosition[ ToString[4^k], ToString[n] ] == {}, k++ ]; a = Append[a, k], {n, 0, 50} ]; a

%t 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 *)

%o (Python)

%o def a(n):

%o target, k, pow4 = str(n), 1, 4

%o while not target in str(pow4): k, pow4 = k+1, pow4*4

%o return k

%o print([a(n) for n in range(72)]) # _Michael S. Branicky_, May 02 2021

%Y Essentially the same as A062521.

%K base,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 10 2001

%E Name edited and more terms from _Michael S. Branicky_, May 02 2021