cp's OEIS Frontend

A280667 a(n) = number of primes of the form 4k + 1 such that 2n - 4k - 1 is prime.

%I A280667 #17 Sep 08 2022 08:46:18
%S A280667 0,0,0,1,1,1,0,2,2,2,2,3,1,2,2,2,3,4,0,3,4,3,4,5,2,3,4,3,5,6,0,5,6,2,
%T A280667 4,6,3,5,6,4,3,8,2,4,6,4,4,7,2,6,8,5,5,8,4,7,10,6,6,12,3,5,10,3,6,9,4,
%U A280667 5,6,7,8,11,3,5,10,4,8,11,2,8,10,5,6,13,6,6,8,7,7,14,2,8,12,5
%N A280667 a(n) = number of primes of the form 4k + 1 such that 2n - 4k - 1 is prime.
%C A280667 Primes p such that a(p) = 0: 2, 3, 7, 19, 31.
%e A280667 a(8) = 2 because 2*8 - 4*1 - 1 = 11 is prime where 4*1 + 1 = 5 is prime of the form 4k+1 and 2*8 - 4*3 - 1 = 3 is prime where 4*3 + 1 = 13 is prime of the form 4k+1.
%o A280667 (Magma)  A280667 := func<n|#[4*k+1: k in [1..(2*n-4) div 4]| IsPrime(4*k+1)  and IsPrime(2*n-4*k-1)]>; [A280667(n):n in[1..100]];
%o A280667 (PARI) a(n) = sum(k=1, 2*n, isprime(k) && isprime(2*n-k) && ((2*n-k) % 4 == 1)); \\ _Michel Marcus_, Jan 07 2017
%Y A280667 Cf. A002144, A035026, A278287, A279027.
%K A280667 nonn
%O A280667 1,8
%A A280667 _Juri-Stepan Gerasimov_, Jan 07 2017