A331853 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise AND operator to the numbers represented by the blocks.

1, 1, 2, 2, 2, 3, 2, 2, 2, 3, 3, 4, 2, 3, 3, 3, 2, 3, 3, 4, 2, 3, 3, 4, 2, 3, 3, 5, 2, 3, 3, 3, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 6, 2, 3, 3, 5, 3, 4, 4, 5, 2, 3, 3, 5, 3, 4, 4, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 6, 2, 3, 3, 4, 3, 4, 4

Offset

0,3

Links

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

Rémy Sigrist, PARI program for A331853

Index entries for sequences related to binary expansion of n

Formula

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

a(2^k-1) = A008619(k+1) for any k >= 0.

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A331851 for similar sequences.

Cf. A008619.

Sequence in context: A109709 A125604 A216685 * A187184 A301375 A325273

Adjacent sequences: A331850 A331851 A331852 * A331854 A331855 A331856

Keyword

nonn,base

Author

Rémy Sigrist, Jan 29 2020

Status

approved