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

1,2

Links

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

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

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)

Maple

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

Mathematica

<<NumberTheory`NumberTheoryFunctions` Table[NextPrime[n+1]-NextPrime[n], {n, 1, 256}]
(* Second program: *)
Abs[Subtract @@ #] & /@ Partition[Array[NextPrime, 105], 2, 1] (* Michael De Vlieger, Jan 03 2019 *)

Prog

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

Crossrefs

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

First differences of A151800.

Cf. also A109578.

Sequence in context: A240183 A112631 A158706 * A231563 A282849 A111813

Adjacent sequences: A096497 A096498 A096499 * A096501 A096502 A096503

Keyword

nonn

Author

Labos Elemer, Jul 09 2004

Status

approved