A326702 Number of distinct vertices in the set-system with BII-number n.

0, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Author

Gus Wiseman, Jul 22 2019

Keywords

• nonn

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. 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.

Examples

			The BII-number of {{1,2},{1,4}} is 260, with distinct vertices {1,2,4}, so a(260) = 3.
		

Crossrefs

Positions of first appearances are A072639.

Cf. A000120, A029931, A048793, A070939, A326031, A326701, A326703, A326704.

Programs

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
Table[Length[Union@@bpe/@bpe[n]],{n,0,100}]