A075761 - OEIS

A075761

Numbers n such that there are at least 3 integers k from the set {2,3,4,5,6,7,8,9} such that the digital sum of each base k representation of n equals k.

%I #4 Oct 12 2013 15:31:16

%S 13,17,19,21,25,29,31,33,37,41,57,61,65,73,85,91,121,129,133,145,169,

%T 225,253,257,261,265,281,301,325,337,361,385,505,513,757,785,841,1057,

%U 1081,1093,1381,1625,2080,2241,3241,4117,4377,4401,5125,8281,16416

%N Numbers n such that there are at least 3 integers k from the set {2,3,4,5,6,7,8,9} such that the digital sum of each base k representation of n equals k.

%C 13, 33, 37 and 57 work for 4 bases. 85 is the only integer found that works for 5 bases: 3, 4, 5, 7 and 8.

%e 91 in base 3 = 10101 and 1 + 0 + 1 + 0 + 1 = 3, which is the base. 91 in base 6 = 231 and 2 + 3 + 1 = 6, which is the base. 91 in base 7 = 160 and 1 + 6 + 0 = 7, which is the base.

%K base,nonn

%O 1,1

%A _Paul Lusch_, Oct 08 2002