A239834 - OEIS

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A239834

a(n) is the smallest k such that the first n powers of k have an even number of digits in base 10.

10, 32, 47, 57, 64, 69, 72, 75, 78, 80, 82, 83, 84, 85, 86, 87, 88, 88, 89, 90, 90, 91, 91, 91, 92, 92, 92, 93, 93, 93, 93, 94, 94, 94, 94, 94, 94, 95, 95, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 97, 97, 97, 97

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The smallest term with 4 digits is a(230) = 9901 and the smallest with 6 digits is a(23025) = 999901.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 47 because 47 is the smallest n such that n, n^2 and n^3 (here 47, 2209 and 103823) have an even number of digits.

MATHEMATICA

a[n_] := a[n] = Block[{k = If[n == 1, 10, a[n-1]]}, While[! And @@ EvenQ[ IntegerLength[ k^Range[n]]], k++]; k]; Array[a, 100]

CROSSREFS