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

1,1

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.

Links

Table of n, a(n) for n=1..66.

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

Example

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.

Prog

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

Crossrefs

Cf. A062051, A096304.

Sequence in context: A047275 A047590 A146329 * A133893 A101647 A155150

Adjacent sequences: A272341 A272342 A272343 * A272345 A272346 A272347

Keyword

nonn

Author

Tom Edgar, Apr 26 2016

Status

approved