A375486 a(n) is the number of integers k between 0 and n such that n OR k is a prime number (where OR denotes the bitwise OR operator).

0, 0, 3, 4, 2, 6, 3, 8, 2, 4, 3, 8, 3, 8, 0, 0, 5, 12, 7, 16, 7, 14, 11, 24, 6, 12, 6, 12, 14, 30, 15, 32, 7, 14, 6, 12, 9, 20, 4, 8, 13, 28, 17, 36, 11, 22, 15, 32, 9, 18, 6, 12, 13, 28, 0, 0, 14, 28, 15, 32, 15, 32, 0, 0, 13, 26, 15, 32, 13, 26, 19, 40, 14

Offset

0,3

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, Scatterplot of (n, k) such that 0 <= k <= n <= 1024 and n OR k is prime

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  ------------------------
   0     0  None
   1     0  None
   2     3  0, 1, 2
   3     4  0, 1, 2, 3
   4     2  1, 3
   5     6  0, 1, 2, 3, 4, 5
   6     3  1, 3, 5
   7     8  0, 1, 2, 3, 4, 5, 6, 7
   8     2  3, 5
   9     4  2, 3, 4, 5
  10     3  1, 3, 9
  11     8  0, 1, 2, 3, 8, 9, 10, 11
  12     3  1, 5, 9
  13     8  0, 1, 4, 5, 8, 9, 12, 13
  14     0  None
  15     0  None

Prog

(PARI) a(n) = sum(k = 0, n, isprime(bitor(n, k)))

Crossrefs

Cf. A375485 (XOR variant), A375487 (AND variant).

Sequence in context: A154570 A145961 A369557 * A082928 A139524 A247413

Adjacent sequences: A375483 A375484 A375485 * A375487 A375488 A375489

Keyword

nonn,base,easy

Author

Rémy Sigrist, Aug 17 2024

Status

approved