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%I #5 Apr 27 2016 04:47:55
%S 6,7,8,15,16,17,18,19,20,21,22,23,24,25,26,33,34,35,42,43,44,45,46,47,
%T 48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
%U 71,72,73,74,75,76,77,78,79,80,87,88,89,96,97,98,99,100,101
%N Positive integers n where the number of parts function on the set of 3-ary partitions of n is equidistributed mod 3.
%C An integer n is in the list if and only if n_i=2 for some index i>0 where n = Sum_{i>=0}n_i3^i is the base 3 representation of n.
%C Appears to be the complement of A096304.
%H Tom Edgar, <a href="http://arxiv.org/abs/1603.00085">The distribution of the number of parts of m-ary partitions modulo m.</a>, arXiv:1603.00085 [math.CO], 2016.
%e There are three 3-ary partitions of 6: one has 2 parts (3+3), one has 4 parts (3+1+1+1), and one has 6 parts (1+1+1+1+1+1); thus, modulo 3, the number of parts function is equidistributed mod 3 and so 6 is a term.
%e There are five 3-ary partitions of 9 so the number of parts function cannot be equidistributed mod 3. Thus, 9 is not a term.
%o (Sage) M=[n for n in [1..105] if (2) in n.digits(3)[1:]]
%Y Cf. A062051, A096304.
%K nonn
%O 1,1
%A _Tom Edgar_, Apr 26 2016