A086155 - OEIS

%I #9 Nov 19 2017 01:47:09

%S 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,

%T 14,15,16,16,17,18,17,18,19,19,20,19,20,21,19,20,21,22,22,23,24,24,25,

%U 26,26,27,23,24,25,25,26,27,28,28,29,28,29,30,31,29,30,30,31,32,33,32

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

%C 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.

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

%e n=50: d=2n=100, p=A020483(50)=3 because by definition, 3 is

%e the least prime so that p and p+100=103 are both primes;

%e a(50) here corresponds to the number of primes between

%e {p,p+100} = {3,103} not counting borders of interval;

%e thus a(50)=24, size of {5,7,...,97,101}.

%t 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}]

%Y Cf. A020483, A000720, A086153.

%K nonn

%O 1,4

%A _Labos Elemer_, Aug 08 2003