A072325 Number of even numbers that cannot be expressed as the difference p-q of two odd primes q < p <= prime(n).

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

Offset: 2

Author

T. D. Noe, Jul 15 2002, Nov 19 2006

Keywords

• easy
• nonn

Comments

If a(n)=0, then Prime[n], called a cluster prime, is in A038134. If a(n)>0 then Prime[n] is in A038133.

Examples

			a(25)=1 because Prime[25]=97 and there is 1 even number, 88, that cannot be written as the difference of two odd primes less than or equal to 97.
		

Links

• Eric Weisstein's World of Mathematics, Cluster Primes

Crossrefs

Cf. A038133, A038134.

Programs

Mathematica

m=10000; n=PrimePi[m]-1; p=Table[Prime[i+1], {i, n}]; d=Table[0, {m/2}]; c=Table[0, {n}]; For[i=2, i<=n, i++, For[j=1, j