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

0,4

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.

Links

Table of n, a(n) for n=0..86.

Example

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

Mathematica

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

Crossrefs

Positions of first appearances are A072639.

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

Sequence in context: A346953 A235508 A271778 * A133563 A104518 A329030

Adjacent sequences: A326699 A326700 A326701 * A326703 A326704 A326705

Keyword

nonn

Author

Gus Wiseman, Jul 22 2019

Status

approved