editing

approved

Case n=1 is degenerate as 1*pprime(1)=2, 1*pprime(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.

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

Number of primes between n*pprime(n) and n*pprime(n+1).

Case n=1 is degenerate as 1p1*p(1)=2, 1p1*p(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.

a(n) = pi(n*prime(n+1)) - pi(n*prime(n)) for n > 1 with a(1) = 0. - Wesley Ivan Hurt, Dec 27 2023

a(4)=5 because between 4p4*p(4)=4*7=28 and 4p4*p(5)=4*11=44, there are exactly 5 primes: 29,31,37,41,43.

Cf. A000040, A000720, A102820.

approved

editing

_Zak Seidov (zakseidov(AT)yahoo.com), _, Feb 28 2005

Case n=1 is degenerate as 1p(1)=2, 1p(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.

nonn,new

nonn

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

nonn,new

nonn

Number of primes between n*p(n) and n*p(n+1).

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, 52, 14, 23, 6, 40, 8, 26, 24, 22, 27, 26, 6, 45, 13, 19, 8, 63, 60, 21, 9, 18, 34, 13, 56, 35, 33, 36, 12, 37, 24, 13, 62, 81, 31, 16, 26, 97, 37, 67, 15, 24, 43, 59, 41, 47, 37, 44, 58

1,3

Case n=1 is degenerate as 1p(1)=2, 1p(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.

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

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

Cf. A102820.

nonn

Zak Seidov (zakseidov(AT)yahoo.com), Feb 28 2005

approved