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A375487
a(n) is the number of integers k between 0 and n such that n AND k is a prime number (where AND denotes the bitwise AND operator).
3
0, 0, 1, 2, 0, 1, 2, 4, 0, 0, 4, 5, 0, 3, 2, 6, 0, 1, 8, 10, 0, 6, 4, 11, 0, 4, 4, 10, 0, 7, 2, 11, 0, 0, 16, 16, 0, 9, 8, 17, 0, 1, 8, 14, 0, 12, 4, 16, 0, 8, 8, 16, 0, 13, 4, 17, 0, 8, 4, 15, 0, 15, 2, 18, 0, 0, 32, 33, 0, 16, 16, 34, 0, 1, 16, 27, 0, 18, 8
OFFSET
0,4
FORMULA
a(n) = 0 iff n = 0 or n belongs to A102210.
a(2^k-1) = A000720(2^k-1) for any k > 0.
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
-- ---- ------------------
0 0 None
1 0 None
2 1 2
3 2 2, 3
4 0 None
5 1 5
6 2 2, 3
7 4 2, 3, 5, 7
8 0 None
9 0 None
10 4 2, 3, 6, 7
11 5 2, 3, 6, 7, 11
12 0 None
13 3 5, 7, 13
14 2 2, 3
15 6 2, 3, 5, 7, 11, 13
PROG
(PARI) a(n) = sum(k = 0, n, isprime(bitand(n, k)))
CROSSREFS
Cf. A000720, A102210, A117494, A375485 (XOR variant), A375486 (OR variant).
Sequence in context: A354773 A368724 A304784 * A354665 A131644 A115346
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Aug 17 2024
STATUS
approved