A331851 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then multiplying the numbers represented by the blocks.

1, 1, 2, 2, 2, 4, 3, 3, 2, 5, 4, 7, 3, 7, 4, 5, 2, 6, 5, 9, 4, 7, 7, 11, 3, 9, 7, 11, 4, 11, 6, 7, 2, 7, 6, 11, 5, 11, 9, 14, 4, 11, 7, 15, 7, 15, 11, 17, 3, 11, 9, 13, 7, 15, 11, 19, 4, 14, 11, 19, 6, 17, 8, 11, 2, 8, 7, 13, 6, 13, 11, 17, 5, 10, 11, 21, 9

Offset

0,3

Comments

This sequence is a variant of A321318.

Links

Table of n, a(n) for n=0..76.

Rémy Sigrist, PARI program for A331851

Index entries for sequences related to binary expansion of n

Formula

a(2^k) = 2 for any k > 0.

a(2^k+1) = k+2 for any k > 1.

Example

For n = 6:
- the binary representation of 6 is "110",
- we can split it in 4 ways:
      "110" -> 6
      "1" and "10" -> 1*2 = 2
      "11" and "0" -> 3*0 = 0
      "1" and "1" and "0" -> 1*1*0 = 0
- we have 3 distinct values,
- hence a(6) = 3.

Prog

(PARI) See Links section.

Crossrefs

Cf. A321318 (additive variant).

Cf. A331852 (XOR variant), A331853 (AND variant), A331854 (OR variant).

Cf. A331855 (reverse variant).

Sequence in context: A358527 A257126 A050493 * A335607 A366192 A347628

Adjacent sequences: A331848 A331849 A331850 * A331852 A331853 A331854

Keyword

nonn,base

Author

Rémy Sigrist, Jan 29 2020

Status

approved