A105161 Difference between n and the second-smallest prime larger than n.

3, 2, 3, 4, 3, 6, 5, 6, 5, 4, 3, 6, 5, 6, 5, 4, 3, 6, 5, 10, 9, 8, 7, 8, 7, 6, 5, 4, 3, 8, 7, 10, 9, 8, 7, 6, 5, 6, 5, 4, 3, 6, 5, 10, 9, 8, 7, 12, 11, 10, 9, 8, 7, 8, 7, 6, 5, 4, 3, 8, 7, 10, 9, 8, 7, 6, 5, 6, 5, 4, 3, 8, 7, 10, 9, 8, 7, 6, 5, 10, 9, 8, 7, 14, 13, 12, 11, 10, 9, 12, 11, 10, 9, 8, 7, 6, 5

Offset: 0

Author

Zak Seidov, Apr 29 2005

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A101300.

Programs

Maple

with(numtheory); A105161:=n->ithprime(pi(n) + 2); seq(A105161(n), n=0..100); # Wesley Ivan Hurt, Feb 26 2014

Mathematica

Table[Prime[PrimePi[n] + 2], {n, 0, 100}] (* Wesley Ivan Hurt, Feb 26 2014 *)

PARI

a(n) = prime(primepi(n)+2) - n; \\ Michel Marcus, Oct 09 2013

PARI

a(n)=nextprime(nextprime(n+1)+1)-n \\ Charles R Greathouse IV, Oct 09 2013

Python

from sympy import nextprime
def a(n): return nextprime(nextprime(n)) - n
print([a(n) for n in range(97)]) # Michael S. Branicky, Mar 02 2021

Formula

a(n) = prime(pi(n)+2) - n.