A072680 Difference between (least prime >= n) and (largest prime <= n).

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

Offset: 2

Author

Reinhard Zumkeller, Jul 01 2002

Keywords

• nonn

Comments

a(n) = 0 iff n is prime.

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537

Crossrefs

Cf. A007917, A007918, A013633, A072681, A097106.

Programs

Mathematica

f[n_]:=If[PrimeQ[n],0,NextPrime[n]-NextPrime[n,-1]];Array[f,110,2] (* Harvey P. Dale, Sep 22 2011 *)

MuPAD

numlib::prevprime(i)*(-1)-nextprime(i)*(-1)$ i = 2..106 // Zerinvary Lajos, Feb 26 2007

PARI

A072680(n) = (nextprime(n) - precprime(n)); \\ Antti Karttunen, Sep 23 2018

Formula

a(n) = A007918(n) - A007917(n).

a(n) = A057427(n - A007917(n)) * A001223(A049084(A007917(n))).