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A140199 a(n) = the number of pairs of (not necessarily distinct) positive integers j and k where j <= n and k <= n such that k+j is prime.

%I A140199 #11 Mar 21 2021 19:09:28
%S A140199 1,2,3,5,6,8,10,12,15,19,22,26,29,32,36,41,45,49,53,57,62,68,73,79,85,
%T A140199 91,98,105,111,118,125,132,139,147,155,164,173,182,191,201,210,220,
%U A140199 229,238,248,258,267,276,286,296,307,319,330,342,355,368,382,396,409,422
%N A140199 a(n) = the number of pairs of (not necessarily distinct) positive integers j and k where j <= n and k <= n such that k+j is prime.
%F A140199 a(n) = sum{k=1 to n} A108954(k). (A108954(n) = pi(2n)-pi(n), where pi(n) is the number of primes that are <= n). a(n) = A071917(n)+1.
%e A140199 For n = 4 there are 5 pairs of positive integers, each <= n=4, that sum to a prime: 1+1=2, 1+2=3, 2+3=5, 1+4=5 and 3+4=7.
%p A140199 A108954 := proc(n) numtheory[pi](2*n)-numtheory[pi](n) ; end: A140199 := proc(n) add( A108954(k),k=1..n) ; end: seq(A140199(n),n=1..80) ; # _R. J. Mathar_, Jun 19 2008
%t A140199 Table[Count[Union[Sort/@Tuples[Range[n],{2}]],_?(PrimeQ[Total[#]]&)],{n,60}] (* _Harvey P. Dale_, Mar 21 2021 *)
%Y A140199 Cf. A108954, A071917.
%K A140199 nonn
%O A140199 1,2
%A A140199 _Leroy Quet_, Jun 15 2008
%E A140199 More terms from _R. J. Mathar_, Jun 19 2008