A038607 a(n) is the smallest prime number k such that k > n*pi(k), where pi(k) denotes the prime counting function.

2, 11, 37, 127, 347, 1087, 3109, 8419, 24317, 64553, 175211, 480881, 1304707, 3523901, 9558533, 25874843, 70115473, 189961529, 514272533, 1394193607, 3779851091, 10246935679, 27788566133, 75370121191, 204475052401, 554805820711, 1505578023841, 4086199302113, 11091501631019, 30109570413007

Offset: 1

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jul 1998

Keywords

• nonn
• nice

Comments

a(n) is about exp(n+1+1/(n+1)). - Charles R Greathouse IV, Sep 05 2011

Examples

			For n=1, a(1) = 2, since 2 > 1*pi(2) = 1*1. - _N. J. A. Sloane_, Dec 09 2020
For n=3, the 12th prime (37) is the first one satisfying p(k) > 3k.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A038606, A038623.

Programs

Mathematica

k = 1; Do[ While[ Prime[k] < n*k, k++ ]; Print[Prime[k]], {n, 1, 25} ]

PARI

k=1;n=1;forprime(p=3,4e9,if(p/n++>k,print1(p", ");k++)) \\ Charles R Greathouse IV, Sep 06 2011

Formula

a(n) = prime(A038606(n)) = A000040(A038606(n)).

Extensions

Extended by Robert G. Wilson v and Ray Chandler, Dec 01 2004

a(26)-a(30) from Charles R Greathouse IV, Sep 05 2011, Sep 06 2011

a(31)-a(50) obtained from the values of A038625 computed by Jan Büthe. - Giovanni Resta, Sep 01 2018