A331852 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise XOR operator to the numbers represented by the blocks.

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 9, 9, 10, 10, 9, 9, 10, 10, 11, 11, 11, 11, 9, 9, 8, 8, 7, 7, 10, 10, 10, 10, 11, 11, 10, 10, 11, 11, 11, 11, 12

Offset

0,3

Links

Table of n, a(n) for n=0..78.

Rémy Sigrist, PARI program for A331852

Index entries for sequences related to binary expansion of n

Formula

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

Apparently a(2^k-1) = A038348(k) 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 XOR 2 = 3
      "11" and "0" -> 3 XOR 0 = 3
      "1" and "1" and "0" -> 1 XOR 1 XOR 0 = 0
- we have 3 distinct values,
- hence a(6) = 3.

Prog

(PARI) See Links section.

Crossrefs

See A331851 for similar sequences.

Cf. A038348.

Sequence in context: A182008 A375024 A106457 * A379771 A103128 A156080

Adjacent sequences: A331849 A331850 A331851 * A331853 A331854 A331855

Keyword

nonn,base

Author

Rémy Sigrist, Jan 29 2020

Status

approved