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%I #40 Apr 28 2023 21:39:42
%S 2,3,3,8,5,10,8,12,10,19,23,23,16,31,16,36,42,26,31,48,23,48,59,42,39,
%T 71,35,62,108,53,59,96,38,83,108,91,77,127,76,107,178,85,92,217,66,
%U 127,169,87,148,204,121,148,196,134,165,268,122,168,358,136,145,340,111,219,323,206,157,282,255,272,373,246,175,486,132,260,419
%N Consider all pairs of primes (p,q) with p+q = 2n, p <= q; a(n) is the sum of all the p's.
%F a(n) = Sum_{i=1..n} i * c(i) * c(2*n-i), where c = A010051. - _Wesley Ivan Hurt_, Apr 29 2021
%F a(n) = sopf(A362641(n)), n>=2. - _Wesley Ivan Hurt_, Apr 28 2023
%e 2*5 = 10 can be expressed as the sum of two primes in two ways, 3+7 and 5+5, so a(5) = 3+5 = 8.
%p with(numtheory);
%p a:=n-> sum( (i)*( ((pi(i) - pi(i-1)) * (pi(2*n-i) - pi(2*n-i-1))) ), i = 1..n ); seq(a(k),k=1..100); # _Wesley Ivan Hurt_, Jan 20 2013
%o (PARI) a(n) = my(s=0); forprime(p=1, n, if (isprime(2*n-p), s += p)); s; \\ _Michel Marcus_, Apr 29 2021
%Y Cf. A045917, A187129, A186201, A362641.
%K nonn
%O 2,1
%A _N. J. A. Sloane_, Mar 11 2011