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

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, 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, 17, 9, 10, 16, 9, 9, 15, 12, 7, 19, 9, 7, 19, 9, 12, 17, 8, 14

Offset: 1

Author

James D. Klein, Dec 19 2011

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Extension of A002375.

Bisection of A092953.

Programs

Mathematica

Table[Length[Select[Prime[Range[PrimePi[2*n]]], PrimeQ[2*n + #] &]], {n, 100}] (* T. D. Noe, Apr 16 2013 *)

PARI

a(n)=my(s);forprime(p=2,2*n,s+=isprime(2*n+p));s \\ Charles R Greathouse IV, Dec 19 2011
(C++)
#include 
using namespace std;
int main()
{ 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};
  int count, istart = 2;
  for(int n=1; n<=25; n++)
  {
      if(2*n>p[istart]) istart++;
      count = 0;
      for(int j=1; p[j]<2*n; j++)
        for(int i=istart; p[i]-p[j]<=2*n; i++)
          if(p[i]-p[j]==2*n) count++;
      cout << n << ". " << count << endl;
  }
    return 0;
} // code for the first 25 integers, James D. Klein, Dec 21 2011

Formula

a(n) = A092953(2*n). - Bill McEachen, May 24 2024