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

0,1

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A101300.

Sequence in context: A349351 A147658 A221529 * A275769 A094365 A272886

Adjacent sequences: A105158 A105159 A105160 * A105162 A105163 A105164

Keyword

nonn,easy

Author

Zak Seidov, Apr 29 2005

Status

approved