A331854 a(n) is the number of distinct values obtained by partitioning the binary representation of n into consecutive blocks, and then applying the bitwise OR operator to the numbers represented by the blocks.

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 5, 5, 4, 4, 5, 5, 7, 6, 7, 6, 7, 6, 7, 7, 8, 7, 7, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 8, 9, 8, 9, 7, 10, 9, 9, 8, 9, 9, 11, 10, 10, 9, 11, 10, 11, 11, 11, 10, 9, 9, 6, 6, 7, 7, 11, 10, 12, 10, 12, 11, 12, 10, 14, 10, 13, 11, 11

Offset

0,3

Links

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

Rémy Sigrist, PARI program for A331854

Index entries for sequences related to binary expansion of n

Formula

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

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

Prog

(PARI) See Links section.

Crossrefs

See A331851 for similar sequences.

Sequence in context: A156251 A116458 A354166 * A093875 A329242 A266193

Adjacent sequences: A331851 A331852 A331853 * A331855 A331856 A331857

Keyword

nonn,base

Author

Rémy Sigrist, Jan 29 2020

Status

approved