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

Author

Rémy Sigrist, Jan 29 2020

Keywords

• nonn
• base

Examples

			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.
		

Links

• Rémy Sigrist, PARI program for A331853
• Index entries for sequences related to binary expansion of n

Crossrefs

See A331851 for similar sequences.

Cf. A008619.

Programs

PARI

See Links section.

Formula

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

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