OFFSET

1,3

COMMENTS

A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. A set-system is a finite set of finite nonempty sets. 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.

EXAMPLE

The terms together with the corresponding set-systems begin:

0: {}

1: {{1}}

2: {{2}}

3: {{1},{2}}

5: {{1},{1,2}}

6: {{2},{1,2}}

8: {{3}}

9: {{1},{3}}

10: {{2},{3}}

11: {{1},{2},{3}}

13: {{1},{1,2},{3}}

14: {{2},{1,2},{3}}

17: {{1},{1,3}}

19: {{1},{2},{1,3}}

21: {{1},{1,2},{1,3}}

22: {{2},{1,2},{1,3}}

24: {{3},{1,3}}

26: {{2},{3},{1,3}}

28: {{1,2},{3},{1,3}}

34: {{2},{2,3}}

35: {{1},{2},{2,3}}

37: {{1},{1,2},{2,3}}

MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Select[Range[0, 100], Length[bpe[#]]==Length[Union@@bpe/@bpe[#]]&]

CROSSREFS

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 12 2023

STATUS

approved