A247889 Least number k > 0 such that digsum(n^k) = n, or 0 if no such k exists.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 13, 0, 4, 0, 0, 4, 3, 3, 4, 0, 0, 7, 0, 0, 7, 5, 4, 0, 0, 0, 13, 0, 0, 7, 0, 6, 5, 0, 0, 0, 0, 0, 0, 7, 6, 0, 0, 0, 7, 0, 0, 0, 0, 8, 6, 0, 0, 0, 7, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 17, 9, 10, 0, 0, 10, 13, 0, 0, 0, 19, 14, 0, 0, 10, 0, 0, 10, 11, 0, 0

Offset: 0

Author

Derek Orr, Sep 25 2014

Keywords

• nonn
• base

Comments

a(10^n) = 0 for all n > 0.

a(n) = 0 if and only if n is in A124367, complement of A124359.

The PARI code uses that, if sumdigit(n^k) <> n until sumdigits(n^k) > 2n for the first time, then sumdigits(n^k) <> n for all larger k. This might not be true for all n, although statistically sumdigits(n^k) ~ 4.5*log_10(n')*k within a few % (n' = n with trailing 0's removed), when k is not too small. - M. F. Hasler, May 18 2017

Links

• Hans Havermann, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A124359 (a(n) > 0), A124367 (a(n) = 0), A007953, A152147.

Programs

PARI

A247889(n,L=2*n)= if(n<10||vecmin(digits(n-1))==9,return(n<10));k=1;while(L >= s=sumdigits(n^k),if(s,return(k));k++) \\ Renamed to A247889 for use in A124359, A124367 (and elsewhere?), and minor edits by M. F. Hasler, May 18 2017
apply(A247889,[0..100])

Extensions

Data corrected (initial 1 removed, terminal 0 added) by Hans Havermann, Jul 13 2018