A086137 Number of primes between p and p+8 if p is prime, i.e., number of primes between 8+A023202(n) and A023202(n).

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

Offset: 1

Author

Labos Elemer, Jul 29 2003

Keywords

• nonn

Examples

			a(n)=0,1,2 correspond to {p,p+8} prime-pairs either consecutive or pairs with various d-patterns as follows:
a(n)=0 to 89[8]97; a(n)=1 for 29[2,6]37, 53[6,2];
a(n)=2 for 101[2,4,2]109 and once to 3[2,2,4]11.
		

Crossrefs

Cf. A023302, A046133, A048136, A052165.

Programs

Mathematica

cp[x_,y_] := Count[Table[PrimeQ[i],{i,x,y}],True] Do[s=Prime[n]; s1=Prime[n+1]; If[PrimeQ[s+d],k=k+1; Print[cp[s+1,s+d-1]]],{n,1,1000}]; k