A272270 Positive integers n where the number of parts function on the set of 4-ary partitions of n is equidistributed mod 4.

12, 13, 14, 15, 28, 29, 30, 31, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 76, 77, 78, 79, 92, 93, 94, 95, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 140, 141, 142, 143

Offset

1,1

Comments

An integer n is in the list if and only if n_i=3 for some index i>0 where n = Sum_{i>=0}n_i4^i is the base 4 representation of n.

Links

Table of n, a(n) for n=1..60.

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

Example

There are four 4-ary partitions of 12: one has 12 parts (1+1+1+1+1+1+1+1+1+1+1+1), one has 3 parts (4+4+4), one has 9 parts (4+1+1+1+1+1+1+1+1), and one has 6 parts (4+4+1+1+1+1); thus, modulo 4, the number of parts function is equidistributed mod 4 and so 12 is a term.
There are six 4-ary partitions of 16 so the number of parts function cannot be equidistributed mod 4. Thus, 16 is not a term.

Prog

(Sage) [n for n in [1..150] if 3 in n.digits(4)[1:]]

Crossrefs

Cf. A005705, A272344.

Sequence in context: A331214 A364733 A270041 * A133894 A209725 A045879

Adjacent sequences: A272267 A272268 A272269 * A272271 A272272 A272273

Keyword

nonn

Author

Tom Edgar, Apr 28 2016

Status

approved