A096501 Difference between primes preceding n+1 and n.

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

Offset: 1

Author

Labos Elemer, Jul 09 2004

Keywords

• nonn

Comments

Values a(1) = 0 and a(2) = 4 are based on convention in Mathematica-language that PreviousPrime(1) = PreviousPrime(2) = -2. - Antti Karttunen, Jan 03 2019

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A000720, A001223, A010051, A096500, A136548, A151799, A175851, A007917.

Programs

Maple

0,4,seq(prevprime(n+1)-prevprime(n),n=3..150); # Muniru A Asiru, Jan 03 2019

Mathematica

Table[NextPrime[n+1, -1] - NextPrime[n, -1], {n, 1, 256}]
Differences[NextPrime[Range[110],-1]] (* Harvey P. Dale, Jul 09 2017 *)

PARI

A136548(n) = if(n<3,1,precprime(n-1));
A096501(n) = if(2==n,4,A136548(1+n)-A136548(n)); \\ Antti Karttunen, Jan 03 2019

Formula

For n > 2, a(n) = A010051(n) * A001223(A000720(n)-1) = A136548(1+n)-A136548(n). - Antti Karttunen, Jan 03 2019

a(n) = A007917(n) - A007917(n-1), for n > 2. - Ridouane Oudra, Oct 05 2024