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
Keywords
Examples
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.
Links
- Tom Edgar, The distribution of the number of parts of m-ary partitions modulo m., arXiv:1603.00085 [math.CO], 2016.
Programs
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Sage
[n for n in [1..150] if 3 in n.digits(4)[1:]]
Comments