A062520 3^a(n) is smallest nonnegative power of 3 containing n.

10, 0, 3, 1, 5, 8, 8, 3, 4, 2, 21, 19, 17, 22, 11, 13, 17, 11, 7, 9, 18, 7, 19, 13, 5, 26, 19, 3, 24, 6, 16, 12, 13, 31, 15, 21, 24, 29, 18, 31, 17, 12, 18, 5, 12, 28, 16, 11, 15, 10, 35, 32, 33, 12, 26, 27, 8, 40, 26, 10, 21, 8, 19, 17, 24, 8, 33, 16, 9, 14, 35, 11, 6, 29, 18, 47

Offset: 0

Author

Robert G. Wilson v, Jun 24 2001

Keywords

• base
• nonn

Examples

			a(1) = 0 since 3^0 = 1. a(2) = a(7) = a(27) = 3 because 3^3 = 27.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A030000. Essentially the same as A063566. Cf. A000244.

Programs

Maple

N:= 99:
count:= 1: A["0"]:= 10:
for n from 0 while count <= N do
  S:= convert(3^n,string); nS:= length(S);
  for m from 1 to 2 while count <= N do
    for i from 1 to nS+1-m while count <= N do
      if S[i] <> "0" and not assigned(A[S[i..i+m-1]]) then
         count:= count+1; A[S[i..i+m-1]]:= n;
      fi
    od
  od
od:
seq(A[convert(n,string)],n=0..N); # Robert Israel, Jun 14 2018

Mathematica

Table[k = 0; While[ StringPosition[ ToString[3^k], ToString[n] ] == {}, k++ ]; k, {n, 0, 75} ]

Python

def a(n):
    s, k = str(n), 0
    while s not in str(3**k): k += 1
    return k
print([a(n) for n in range(76)]) # Michael S. Branicky, Oct 04 2021