A111181 a(n) = prime(n) - pi(n).

2, 2, 3, 5, 8, 10, 13, 15, 19, 25, 26, 32, 35, 37, 41, 47, 52, 54, 59, 63, 65, 71, 74, 80, 88, 92, 94, 98, 99, 103, 116, 120, 126, 128, 138, 140, 145, 151, 155, 161, 166, 168, 177, 179, 183, 185, 196, 208, 212, 214, 218, 224, 225, 235, 241, 247, 253, 255, 260, 264

Offset: 1

Author

Cino Hilliard, Oct 22 2005

Keywords

• easy
• nonn

Comments

Conjecture: There will always be an x such that a(x+1) - a(x) = k for k=1,2.. However, x becomes large when k > 70.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040 (prime), A000720 (pi).

Programs

Maple

a:= n-> ithprime(n)-numtheory[pi](n):
seq(a(n), n=1..60);  # Alois P. Heinz, Jan 15 2025

Mathematica

Table[Prime[n]-PrimePi[n],{n,60}] (* Harvey P. Dale, Mar 11 2012 *)

PARI

a(n)=prime(n)-primepi(n) \\ Charles R Greathouse IV, May 29 2013

Formula

a(n) = A000040(n) - A000720(n).