A069879 Number of pairs {i,j} with i different from j; 1<=i<=n; 1<= j <=n such that i+j is a prime number.

0, 2, 4, 8, 10, 14, 18, 22, 28, 36, 42, 50, 56, 62, 70, 80, 88, 96, 104, 112, 122, 134, 144, 156, 168, 180, 194, 208, 220, 234, 248, 262, 276, 292, 308, 326, 344, 362, 380, 400, 418, 438, 456, 474, 494, 514, 532, 550, 570, 590, 612, 636, 658, 682, 708, 734

Offset: 1

Author

Santi Spadaro, May 04 2002

Keywords

• nonn

Crossrefs

Partial sums of 2*A060715(n).

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 0,
      b(n-1)+pi(2*n-1)-pi(n))
    end:
a:= n-> 2*b(n):
seq(a(n), n=1..70);  # Alois P. Heinz, Sep 29 2017

Mathematica

Table[2*Count[Subsets[Range[n],{2}],?(PrimeQ[Total[#]]&)],{n,50}] (* _Harvey P. Dale, Jan 23 2015 *)

Formula

a(n) = 2 * A071917(n). - Alois P. Heinz, Sep 29 2017