A086138 Number of primes between p and p+10 if p is prime, i.e., number of primes somewhere between 10+A023203(n) and A023203(n).

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

Offset

1,1

Links

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

Example

a(n)=0,1,2,3 correspond to {p,p+10} prime-pairs either
consecutive ones or those with various d-patterns like
as follows: a(n)=0 to cases like 139[10]149; a(n)=2 to
7[4,2,4]17 etc.; a(n)=3 to one case 3[2,2,4,2]13 and
a(n)=2 to cases like 31[6,4]37 or 43[4,6]53.

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; d=10

Prog

(PARI) forprime(p=2, 1e5, if(isprime(p+10), print1(isprime(p+2)+isprime(p+4)+isprime(p+6)+isprime(p+8)", "))) \\ Charles R Greathouse IV, May 15 2013

Crossrefs

Cf. A023303, A031928, A031929.

Sequence in context: A077450 A328330 A214878 * A170822 A054546 A065310

Adjacent sequences: A086135 A086136 A086137 * A086139 A086140 A086141

Keyword

nonn

Author

Labos Elemer, Jul 29 2003

Status

approved