A239834 - OEIS

%I #5 Mar 27 2014 18:38:04

%S 10,32,47,57,64,69,72,75,78,80,82,83,84,85,86,87,88,88,89,90,90,91,91,

%T 91,92,92,92,93,93,93,93,94,94,94,94,94,94,95,95,95,95,95,95,95,96,96,

%U 96,96,96,96,96,96,96,96,96,96,97,97,97,97,97,97,97,97,97

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

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

%H Giovanni Resta, <a href="/A239834/b239834.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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]

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Mar 27 2014