A240718 Number of decompositions of 2n into an unordered sum of two primes, one of the two primes less than sqrt(2n-2).

0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 0, 1, 0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 3, 3, 1, 1, 2, 2, 2, 2, 2

Offset: 1

Author

Lear Young, Apr 11 2014

Keywords

• nonn

Examples

			For n = 7, the a(7) = 1 solution is 2*7 = 3 + 11 = 7 + 7; one of these pairs, 3 + 11, contains a number less than sqrt(2*7 - 2).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002375.

Programs

Maple

P:= NULL: A[1]:= 0: nextp:= 2:
for n from 2 to 100 do
 while nextp^2 < 2*n-2 do
   P:= P, nextp;
   nextp:= nextprime(nextp);
 od;
 A[n]:= numboccur(true, map(t -> isprime(2*n-t), [P]))
od:
seq(A[i],i=1..100); # Robert Israel, Apr 30 2019

PARI

a(n)=sum(i=2,primepi(floor(sqrt(2*n-2))),isprime(2*n-prime(i))) \\ Lear Young, Apr 11 2014