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A326784
BII-numbers of regular set-systems.
10
0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 16, 18, 25, 30, 32, 33, 42, 45, 51, 52, 63, 64, 75, 76, 82, 94, 97, 109, 115, 116, 127, 128, 129, 130, 131, 132, 136, 137, 138, 139, 140, 144, 146, 160, 161, 192, 256, 258, 264, 266, 288, 385, 390, 408, 427, 428, 434, 458
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 regular if all vertices appear the same number of times.
EXAMPLE
The sequence of all regular set-systems together with their BII-numbers begins:
0: {}
1: {{1}}
2: {{2}}
3: {{1},{2}}
4: {{1,2}}
7: {{1},{2},{1,2}}
8: {{3}}
9: {{1},{3}}
10: {{2},{3}}
11: {{1},{2},{3}}
12: {{1,2},{3}}
16: {{1,3}}
18: {{2},{1,3}}
25: {{1},{3},{1,3}}
30: {{2},{1,2},{3},{1,3}}
32: {{2,3}}
33: {{1},{2,3}}
42: {{2},{3},{2,3}}
45: {{1},{1,2},{3},{2,3}}
51: {{1},{2},{1,3},{2,3}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SameQ@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]&]
CROSSREFS
Sequence in context: A047549 A039074 A326966 * A047337 A039049 A037466
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved