A305706 - OEIS

A305706

a(n) = smallest m such that the sum of digits of n^m is greater than n, or 0 if no such m exists.

0, 0, 2, 2, 2, 2, 2, 2, 2, 3, 0, 4, 3, 2, 2, 3, 3, 2, 4, 3, 14, 4, 5, 4, 4, 5, 4, 5, 6, 6, 14, 5, 6, 5, 6, 6, 6, 5, 5, 6, 14, 7, 6, 8, 6, 7, 6, 8, 7, 7, 16, 6, 6, 8, 7, 8, 7, 7, 9, 7, 15, 8, 8, 7, 8, 8, 9, 8, 8, 8, 18, 12, 9, 9, 8, 9, 9, 9, 9, 9, 18, 10, 11, 11, 10, 11, 11, 10, 9, 10, 17, 11, 11, 10, 11, 10, 12, 12, 10, 11, 0

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OFFSET

0,3

COMMENTS

a(n) = smallest m such that A007953(n^m) > n, or 0 if no such m exists.

If n is a term of A178501, then a(n) = 0. - Felix Fröhlich, Jun 10 2018

LINKS

Table of n, a(n) for n=0..100.

PROG

(PARI) a(n) = if(sumdigits(n) < 2, return(0), my(m=2); while(1, if(sumdigits(n^m) > n, return(m)); m++)) \\ Felix Fröhlich, Jun 10 2018

CROSSREFS

Cf. A007953, A038206, A178501, A305707.