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A202472 Goldbach's Problem extended to subtraction: number of decompositions of 2n into unordered differences of two primes, p, q, where p < 2n < q.

%I A202472 #23 Jun 12 2024 17:51:18
%S A202472 0,1,1,2,2,3,2,3,3,3,2,6,4,3,6,3,4,6,4,5,8,4,4,7,6,4,9,8,4,11,5,5,11,
%T A202472 6,8,9,4,7,11,7,4,13,7,5,15,7,8,13,8,9,11,7,7,13,10,5,13,7,7,19,9,8,
%U A202472 17,9,10,16,9,9,15,12,7,19,9,7,19,9,12,17,8,14
%N A202472 Goldbach's Problem extended to subtraction: number of decompositions of 2n into unordered differences of two primes, p, q, where p < 2n < q.
%H A202472 T. D. Noe, <a href="/A202472/b202472.txt">Table of n, a(n) for n = 1..10000</a>
%F A202472 a(n) = A092953(2*n). - _Bill McEachen_, May 24 2024
%t A202472 Table[Length[Select[Prime[Range[PrimePi[2*n]]], PrimeQ[2*n + #] &]], {n, 100}] (* _T. D. Noe_, Apr 16 2013 *)
%o A202472 (PARI) a(n)=my(s);forprime(p=2,2*n,s+=isprime(2*n+p));s \\ _Charles R Greathouse IV_, Dec 19 2011
%o A202472 (C++)
%o A202472 #include <iostream>
%o A202472 using namespace std;
%o A202472 int main()
%o A202472 { int p[25] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97};
%o A202472   int count, istart = 2;
%o A202472   for(int n=1; n<=25; n++)
%o A202472   {
%o A202472       if(2*n>p[istart]) istart++;
%o A202472       count = 0;
%o A202472       for(int j=1; p[j]<2*n; j++)
%o A202472         for(int i=istart; p[i]-p[j]<=2*n; i++)
%o A202472           if(p[i]-p[j]==2*n) count++;
%o A202472       cout << n << ". " << count << endl;
%o A202472   }
%o A202472     return 0;
%o A202472 } // code for the first 25 integers, _James D. Klein_, Dec 21 2011
%Y A202472 Extension of A002375.
%Y A202472 Bisection of A092953.
%K A202472 nonn
%O A202472 1,4
%A A202472 _James D. Klein_, Dec 19 2011