A272344 Positive integers n where the number of parts function on the set of 3-ary partitions of n is equidistributed mod 3.

6, 7, 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 87, 88, 89, 96, 97, 98, 99, 100, 101

Offset: 1

Author

Tom Edgar, Apr 26 2016

Keywords

• nonn

Comments

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.

Appears to be the complement of A096304.

Examples

			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.
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.
		

Links

• Tom Edgar, The distribution of the number of parts of m-ary partitions modulo m., arXiv:1603.00085 [math.CO], 2016.

Crossrefs

Cf. A062051, A096304.

Programs

Sage

M=[n for n in [1..105] if (2) in n.digits(3)[1:]]