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A326783 BII-numbers of uniform set-systems. 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 (list; graph; refs; listen; history; text; internal format)
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 set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. A set-system 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 set-systems together with their BII-numbers 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

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Last modified April 13 03:43 EDT 2021. Contains 342934 sequences. (Running on oeis4.)