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A071917 Number of pairs (x,y) where x is even, y is odd, 1<=x<=n, 1<=y<=n and x+y is prime.

%I A071917 #15 Feb 17 2017 19:52:10
%S A071917 0,1,2,4,5,7,9,11,14,18,21,25,28,31,35,40,44,48,52,56,61,67,72,78,84,
%T A071917 90,97,104,110,117,124,131,138,146,154,163,172,181,190,200,209,219,
%U A071917 228,237,247,257,266,275,285,295,306,318,329,341,354,367,381,395,408,421
%N A071917 Number of pairs (x,y) where x is even, y is odd, 1<=x<=n, 1<=y<=n and x+y is prime.
%H A071917 Alois P. Heinz, <a href="/A071917/b071917.txt">Table of n, a(n) for n = 1..20000</a>
%F A071917 a(n) = sum over primes p from 3 to 2n-1 of min(p-1, 2n+1-p)/2.
%F A071917 a(n) = a(n-1) + pi(2*n-1) - pi(n) for n>0, a(0) = 0. - _Alois P. Heinz_, Feb 03 2017
%e A071917 a(6)=7: The sums x+y are 2+1, 2+3, 2+5, 4+1, 4+3, 6+1, 6+5.
%p A071917 with(numtheory):
%p A071917 a:= proc(n) option remember; `if`(n=0, 0,
%p A071917       a(n-1)+pi(2*n-1)-pi(n))
%p A071917     end:
%p A071917 seq(a(n), n=1..70);  # _Alois P. Heinz_, Feb 03 2017
%t A071917 a[n_] := Sum[If[PrimeQ[p], Min[p-1, 2n+1-p]/2, 0], {p, 3, 2n-1}]
%Y A071917 Cf. A000720.
%Y A071917 Column k=2 of A282516.
%K A071917 easy,nonn
%O A071917 1,3
%A A071917 _Enoch Haga_, Jun 13 2002
%E A071917 Edited by _Dean Hickerson_, Jun 18 2002