

A272270


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


0



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
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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 mary partitions modulo m., arXiv:1603.00085 [math.CO], 2016.


EXAMPLE

There are four 4ary 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 4ary partitions of 16 so the number of parts function cannot be equidistributed mod 4. Thus, 16 is not a term.


PROG

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


CROSSREFS

Cf. A005705, A272344.
Sequence in context: A324322 A083826 A270041 * A133894 A209725 A045879
Adjacent sequences: A272267 A272268 A272269 * A272271 A272272 A272273


KEYWORD

nonn


AUTHOR

Tom Edgar, Apr 28 2016


STATUS

approved



