%I #7 Dec 27 2023 13:53:36

%S 0,1,2,5,2,5,2,6,9,2,11,8,3,9,12,14,6,13,12,9,18,11,17,23,9,7,14,8,16,

%T 52,14,23,6,40,8,26,24,22,27,26,6,45,13,19,8,63,60,21,9,18,34,13,56,

%U 35,33,36,12,37,24,13,62,81,31,16,26,97,37,67,15,24,43,59,41,47,37,44,58

%N Number of primes between n*prime(n) and n*prime(n+1).

%C Case n=1 is degenerate as 1*prime(1)=2, 1*prime(2)=3 and between 2 and 3 there is no prime while (PrimePi[n Prime[n+1]]-PrimePi[n Prime[n]]/.n->1) gives 1.

%F a(n) = pi(n*prime(n+1)) - pi(n*prime(n)) for n > 1 with a(1) = 0. - _Wesley Ivan Hurt_, Dec 27 2023

%e a(4)=5 because between 4*prime(4)=4*7=28 and 4*prime(5)=4*11=44, there are exactly 5 primes: 29,31,37,41,43.

%t A104289=Prepend[Table[PrimePi[n Prime[n+1]]-PrimePi[n Prime[n]], {n, 2, 100}], 0]

%Y Cf. A000040, A000720, A102820.

%K nonn

%O 1,3

%A _Zak Seidov_, Feb 28 2005