A086155 a(n) is the number of primes between the primes p = A020483(n) and q = 2n + A020483(n).

0, 1, 1, 2, 3, 3, 4, 5, 5, 6, 5, 6, 7, 8, 7, 8, 9, 9, 10, 11, 11, 12, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 16, 17, 18, 17, 18, 19, 19, 20, 19, 20, 21, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 23, 24, 25, 25, 26, 27, 28, 28, 29, 28, 29, 30, 31, 29, 30, 30, 31, 32, 33, 32

Offset: 1

Author

Labos Elemer, Aug 08 2003

Keywords

• nonn

Comments

a(n) + 1 = 1 + A086154(n) provides the length of the n-th row arising in table of A086153; a(n) <= n/2 holds if n > 22.

Examples

			n=50: d=2n=100, p=A020483(50)=3 because by definition, 3 is
the least prime so that p and p+100=103 are both primes;
a(50) here corresponds to the number of primes between
{p,p+100} = {3,103} not counting borders of interval;
thus a(50)=24, size of {5,7,...,97,101}.
		

Crossrefs

Cf. A020483, A000720, A086153.

Programs

Mathematica

Table[fl=1; Do[s0=Prime[k]; s=2*n+Prime[k]; If[PrimeQ[s]&&Equal[fl,1], Print[PrimePi[s]-k-1]; fl=0],{k,1,200}],{n,1,25}]

Formula

a(n) = Pi(A020483(n)) - Pi(2n + A020483(n)) - 1.