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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved