OFFSET
1,2
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.
Also numbers whose binary indices all belong to A018900.
EXAMPLE
The sequence of all simple labeled graphs together with their BII-numbers begins:
0: {}
4: {{1,2}}
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}}
256: {{1,4}}
260: {{1,2},{1,4}}
272: {{1,3},{1,4}}
276: {{1,2},{1,3},{1,4}}
288: {{2,3},{1,4}}
292: {{1,2},{2,3},{1,4}}
304: {{1,3},{2,3},{1,4}}
308: {{1,2},{1,3},{2,3},{1,4}}
512: {{2,4}}
516: {{1,2},{2,4}}
528: {{1,3},{2,4}}
532: {{1,2},{1,3},{2,4}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SameQ[2, ##]&@@Length/@bpe/@bpe[#]&]
CROSSREFS
Cf. A000120, A006125, A006129, A018900, A048793, A062880, A070939, A309356 (same for MM-numbers), A322551, A326031, A326702.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved