A109578 a(n) = (pi(n+1)-pi(n)) * (prime(n+1)-prime(n)), where pi(k) is the number of prime numbers less than or equal to k (= A000720(k)) and prime(k) is the k-th prime number (= A000040(k)).

1, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 14, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 10, 0, 0, 0, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 14, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 0

Offset: 1

Author

Roger L. Bagula, Jun 29 2005

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001223, A010051.

Cf. also A096500, A096501.

Programs

Maple

with(numtheory): a:=n->(pi(n+1)-pi(n))*(ithprime(n+1)-ithprime(n)): seq(a(n),n=1..160);

Mathematica

an = Table[(PrimePi[n + 1] - PrimePi[n])*(Prime[n + 1] - Prime[n]), {n, 1, 200}]

PARI

A109578(n) = ((primepi(n+1)-primepi(n)) * (prime(n+1)-prime(n))); \\ Antti Karttunen, Jan 03 2019

Formula

a(n) = (A010051(1+n) * A001223(n)). - Antti Karttunen, Jan 03 2019