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.
The enumeration of these set-systems by number of covered vertices is A326881.
EXAMPLE
Most small numbers are in the sequence, but the sequence of non-terms together with the set-systems with those BII-numbers begins:
20: {{1,2},{1,3}}
22: {{2},{1,2},{1,3}}
28: {{1,2},{3},{1,3}}
30: {{2},{1,2},{3},{1,3}}
36: {{1,2},{2,3}}
37: {{1},{1,2},{2,3}}
44: {{1,2},{3},{2,3}}
45: {{1},{1,2},{3},{2,3}}
48: {{1,3},{2,3}}
49: {{1},{1,3},{2,3}}
50: {{2},{1,3},{2,3}}
51: {{1},{2},{1,3},{2,3}}
52: {{1,2},{1,3},{2,3}}
53: {{1},{1,2},{1,3},{2,3}}
54: {{2},{1,2},{1,3},{2,3}}
55: {{1},{2},{1,2},{1,3},{2,3}}
60: {{1,2},{3},{1,3},{2,3}}
61: {{1},{1,2},{3},{1,3},{2,3}}
62: {{2},{1,2},{3},{1,3},{2,3}}
84: {{1,2},{1,3},{1,2,3}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SubsetQ[bpe/@bpe[#], Intersection@@@Select[Tuples[bpe/@bpe[#], 2], Intersection@@#!={}&]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 29 2019
STATUS
approved