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

Author

Rémy Sigrist, Aug 17 2024

Keywords

• nonn
• base
• easy

Examples

			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
		

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

Crossrefs

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

Programs

PARI

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