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

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, 90, 97, 104, 110, 117, 124, 131, 138, 146, 154, 163, 172, 181, 190, 200, 209, 219, 228, 237, 247, 257, 266, 275, 285, 295, 306, 318, 329, 341, 354, 367, 381, 395, 408, 421

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Formula

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

a(n) = a(n-1) + pi(2*n-1) - pi(n) for n>0, a(0) = 0. - Alois P. Heinz, Feb 03 2017

Example

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

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 0,
      a(n-1)+pi(2*n-1)-pi(n))
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Feb 03 2017

Mathematica

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

Crossrefs

Cf. A000720.

Column k=2 of A282516.

Sequence in context: A186388 A058577 A356075 * A338758 A051060 A116650

Adjacent sequences: A071914 A071915 A071916 * A071918 A071919 A071920

Keyword

easy,nonn

Author

Enoch Haga, Jun 13 2002

Extensions

Edited by Dean Hickerson, Jun 18 2002

Status

approved