A096500 Let f(n) = smallest prime > n; a(n) = f(n+1) - f(n).

1, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0

Offset: 1

Author

Labos Elemer, Jul 09 2004

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A000720, A001223, A010051, A096501, A175851.

First differences of A151800.

Cf. also A109578.

Programs

Maple

seq(nextprime(n+1)-nextprime(n),n=1..250); # Muniru A Asiru, Jan 03 2019

Mathematica

<Michael De Vlieger, Jan 03 2019 *)

PARI

A151800(n) = nextprime(1+n);
A096500(n) = (A151800(1+n)-A151800(n)); \\ Antti Karttunen, Jan 03 2019

Formula

From Antti Karttunen, Jan 03 2019: (Start)

a(n) = A151800(n+1) - A151800(n).

a(n) = A010051(1+n) * A001223(A000720(1+n)).

(End)