A111181 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

1,1

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

Formula

Prime(n) = the n-th prime. Pi(x) = number of primes <= x.

Mathematica

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

Prog

(PARI) primexmpix(n, k) = { local(x, y, z); for(x=1, n, y=prime(x)-primepi(x); z=prime(x+1)-primepi(x+1); if(z-y == k, print1(y", ") ) ) }
(PARI) a(n)=prime(n)-primepi(n) \\ Charles R Greathouse IV, May 29 2013

Crossrefs

Sequence in context: A241421 A157176 A276429 * A267419 A076777 A240210

Adjacent sequences: A111178 A111179 A111180 * A111182 A111183 A111184

Keyword

easy,nonn

Author

Cino Hilliard, Oct 22 2005

Status

approved