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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. 5

%I

%S 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 90,97,104,110,117,124,131,138,146,154,163,172,181,190,200,209,219,

%U 228,237,247,257,266,275,285,295,306,318,329,341,354,367,381,395,408,421

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

%H Alois P. Heinz, <a href="/A071917/b071917.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = sum over primes p from 3 to 2n-1 of min(p-1, 2n+1-p)/2.

%F a(n) = a(n-1) + pi(2*n-1) - pi(n) for n>0, a(0) = 0. - _Alois P. Heinz_, Feb 03 2017

%e a(6)=7: The sums x+y are 2+1, 2+3, 2+5, 4+1, 4+3, 6+1, 6+5.

%p with(numtheory):

%p a:= proc(n) option remember; `if`(n=0, 0,

%p a(n-1)+pi(2*n-1)-pi(n))

%p end:

%p seq(a(n), n=1..70); # _Alois P. Heinz_, Feb 03 2017

%t a[n_] := Sum[If[PrimeQ[p], Min[p-1, 2n+1-p]/2, 0], {p, 3, 2n-1}]

%Y Cf. A000720.

%Y Column k=2 of A282516.

%K easy,nonn

%O 1,3

%A _Enoch Haga_, Jun 13 2002

%E Edited by _Dean Hickerson_, Jun 18 2002

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Last modified July 29 01:22 EDT 2021. Contains 346340 sequences. (Running on oeis4.)