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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 16:45 EST 2021. Contains 340247 sequences. (Running on oeis4.)