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A326785 BII-numbers of uniform regular set-systems. 5
0, 1, 2, 3, 4, 8, 9, 10, 11, 16, 32, 52, 64, 128, 129, 130, 131, 136, 137, 138, 139, 256, 288, 512, 528, 772, 816, 1024, 2048, 2052, 2320, 2340, 2580, 2592, 2868, 4096, 8192, 13376, 16384, 32768, 32769, 32770, 32771, 32776, 32777, 32778, 32779, 32896, 32897 (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. Every finite set of finite nonempty sets has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18. Elements of a set-system are sometimes called edges. A set-system is uniform if all edges have the same size, and regular if all vertices appear the same number of times.

LINKS

Table of n, a(n) for n=1..49.

FORMULA

Intersection of A326783 and A326784.

EXAMPLE

The sequence of all uniform regular 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}}

   32: {{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}}

  136: {{3},{4}}

  137: {{1},{3},{4}}

  138: {{2},{3},{4}}

MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Select[Range[0, 1000], SameQ@@Length/@bpe/@bpe[#]&&SameQ@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]&]

CROSSREFS

Cf. A000120, A029931, A048793, A070939, A319056, A319189, A321698, A326031, A326701, A326783 (uniform), A326784 (regular), A326788.

Sequence in context: A069811 A004826 A326783 * A327080 A291621 A329268

Adjacent sequences:  A326782 A326783 A326784 * A326786 A326787 A326788

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 25 2019

STATUS

approved

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Last modified April 17 22:19 EDT 2021. Contains 343071 sequences. (Running on oeis4.)