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%I #9 Aug 18 2024 09:05:13
%S 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,
%T 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,
%U 15,2,18,0,0,32,33,0,16,16,34,0,1,16,27,0,18,8
%N 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).
%H Rémy Sigrist, <a href="/A375487/b375487.txt">Table of n, a(n) for n = 0..8192</a>
%H Rémy Sigrist, <a href="/A375487/a375487.png">Scatterplot of (n, k) such that 0 <= k <= n <= 1024 and n AND k is prime</a>
%F a(n) = 0 iff n = 0 or n belongs to A102210.
%F a(2^k-1) = A000720(2^k-1) for any k > 0.
%e The first terms, alongside the corresponding k's, are:
%e n a(n) k's
%e -- ---- ------------------
%e 0 0 None
%e 1 0 None
%e 2 1 2
%e 3 2 2, 3
%e 4 0 None
%e 5 1 5
%e 6 2 2, 3
%e 7 4 2, 3, 5, 7
%e 8 0 None
%e 9 0 None
%e 10 4 2, 3, 6, 7
%e 11 5 2, 3, 6, 7, 11
%e 12 0 None
%e 13 3 5, 7, 13
%e 14 2 2, 3
%e 15 6 2, 3, 5, 7, 11, 13
%o (PARI) a(n) = sum(k = 0, n, isprime(bitand(n, k)))
%Y Cf. A000720, A102210, A117494, A375485 (XOR variant), A375486 (OR variant).
%K nonn,base,easy
%O 0,4
%A _Rémy Sigrist_, Aug 17 2024