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

1,1

Links

Table of n, a(n) for n=1..105.

Example

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.

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

Crossrefs

Cf. A023302, A046133, A048136, A052165.

Sequence in context: A004571 A204429 A292560 * A085976 A171624 A032548

Adjacent sequences: A086134 A086135 A086136 * A086138 A086139 A086140

Keyword

nonn

Author

Labos Elemer, Jul 29 2003

Status

approved