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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved