A368109 - OEIS

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A368109

Number of ways to choose 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, 8, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 3, 3, 3, 3, 6, 6, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12

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OFFSET

0,5

COMMENTS

First differs from A367912 at a(52) = 8, A367912(52) = 7.

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}.

Run-lengths are all 4 or 8.

LINKS

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

FORMULA

a(n) = Product_{k in A048793(n)} A000120(k).

EXAMPLE

The binary indices of binary indices of 20 are {{1,2},{1,3}}, with choices (1,1), (1,3), (2,1), (2,3), so a(20) = 4.

The binary indices of binary indices of 52 are {{1,2},{1,3},{2,3}}, with choices (1,1,1), (1,1,3), (1,3,2), (1,3,3), (2,1,2), (2,1,3), (2,3,2), (2,3,3), so a(52) = 8.

MATHEMATICA

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

Table[Length[Tuples[bpe/@bpe[n]]], {n, 0, 100}]

CROSSREFS

All entries appear to belong to A003586.

Positions of ones are A253317.

The version for prime indices is A355741, for multisets A355744.

Choosing a multiset (not sequence) gives A367912, firsts A367913.

Positions of first appearances are A368111, sorted A368112.

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, A355731, A355739, A367771, A367905, A367906, A367915.

Sequence in context: A327144 A327051 A367912 * A275301 A282542 A271518

Adjacent sequences: A368106 A368107 A368108 * A368110 A368111 A368112

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 12 2023

STATUS

approved