

A326783


BIInumbers of uniform setsystems.


6



0, 1, 2, 3, 4, 8, 9, 10, 11, 16, 20, 32, 36, 48, 52, 64, 128, 129, 130, 131, 136, 137, 138, 139, 256, 260, 272, 276, 288, 292, 304, 308, 512, 516, 528, 532, 544, 548, 560, 564, 768, 772, 784, 788, 800, 804, 816, 820, 1024, 1088, 2048, 2052, 2064, 2068, 2080
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OFFSET

1,3


COMMENTS

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. A setsystem is uniform if all edges have the same size.
Alternatively, these are numbers whose binary indices all have the same binary weight, where the binary weight of a nonnegative integer is the numbers of 1's in its binary digits.


LINKS

Table of n, a(n) for n=1..55.


EXAMPLE

The sequence of all uniform setsystems together with their BIInumbers begins:
0: {}
1: {{1}}
2: {{2}}
3: {{1},{2}}
4: {{1,2}}
8: {{3}}
9: {{1},{3}}
10: {{2},{3}}
11: {{1},{2},{3}}
16: {{1,3}}
20: {{1,2},{1,3}}
32: {{2,3}}
36: {{1,2},{2,3}}
48: {{1,3},{2,3}}
52: {{1,2},{1,3},{2,3}}
64: {{1,2,3}}
128: {{4}}
129: {{1},{4}}
130: {{2},{4}}
131: {{1},{2},{4}}


MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SameQ@@Length/@bpe/@bpe[#]&]


CROSSREFS

Cf. A000120, A029931, A048793, A070939, A047966, A306017, A306021, A319269, A320324, A326031, A326784 (regular), A326785 (uniform regular), A326788.
Sequence in context: A047338 A069811 A004826 * A326785 A327080 A291621
Adjacent sequences: A326780 A326781 A326782 * A326784 A326785 A326786


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jul 25 2019


STATUS

approved



