A367912 Number of multisets that can be obtained by choosing a binary index of each binary index of n.

1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 4, 4, 4, 4, 7, 7, 7, 7, 3, 3, 3, 3, 5, 5, 5, 5, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8

Offset

0,5

Comments

A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, 18 has reversed binary expansion (0,1,0,0,1) and binary indices {2,5}.

The run-lengths are all 4 or 8.

Links

Table of n, a(n) for n=0..87.

Example

The binary indices of binary indices of 52 are {{1,2},{1,3},{2,3}}, with multiset choices {1,1,2}, {1,1,3}, {1,2,2}, {1,2,3}, {1,3,3}, {2,2,3}, {2,3,3}, so a(52) = 7.

Mathematica

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

Crossrefs

Positions of ones are A253317.

The version for multisets and divisors is A355733, for sequences A355731.

The version for multisets is A355744, for sequences A355741.

For a sequence of distinct choices we have A367905, firsts A367910.

Positions of first appearances are A367913, sorted A367915.

Choosing a sequence instead of multiset gives A368109, firsts A368111.

Choosing a set instead of multiset gives A368183, firsts A368184.

A048793 lists binary indices, length A000120, sum A029931.

A058891 counts set-systems, covering A003465, connected A323818.

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

Cf. A072639, A309326, A326031, A326702, A326753, A355735, A355739, A355740, A355745, A367771, A367906.

Sequence in context: A037805 A327144 A327051 * A368109 A275301 A282542

Adjacent sequences: A367909 A367910 A367911 * A367913 A367914 A367915

Keyword

nonn

Author

Gus Wiseman, Dec 12 2023

Status

approved