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A375485
a(n) is the number of integers k between 0 and n such that n XOR k is a prime number (where XOR denotes the bitwise XOR operator).
3
0, 0, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 4, 4, 6, 6, 5, 5, 7, 7, 7, 7, 9, 9, 7, 7, 9, 9, 9, 9, 11, 11, 7, 7, 9, 9, 9, 9, 11, 11, 9, 9, 11, 11, 11, 11, 13, 13, 12, 12, 14, 14, 14, 14, 16, 16, 14, 14, 16, 16, 16, 16, 18, 18, 13, 13, 15, 15, 15, 15, 17, 17, 15, 15, 17
OFFSET
0,3
FORMULA
Empirically, if 2^k <= n < 2^(k+1) then a(n) + a(A054429(n)) only depends on k.
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
-- ---- -------------------
0 0 None
1 0 None
2 2 0, 1
3 2 0, 1
4 2 1, 3
5 2 0, 2
6 4 1, 3, 4, 5
7 4 0, 2, 4, 5
8 2 3, 5
9 2 2, 4
10 4 1, 7, 8, 9
11 4 0, 6, 8, 9
12 4 1, 7, 9, 11
13 4 0, 6, 8, 10
14 6 3, 5, 9, 11, 12, 13
15 6 2, 4, 8, 10, 12, 13
PROG
(PARI) a(n) = sum(k = 0, n, isprime(bitxor(n, k)))
CROSSREFS
Cf. A054429, A375486 (OR variant), A375487 (AND variant).
Sequence in context: A125913 A122386 A051464 * A151565 A060632 A160407
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Aug 17 2024
STATUS
approved