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

1,1

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A038606, A038623.

Sequence in context: A178138 A220888 A289616 * A079009 A097651 A320540

Adjacent sequences: A038604 A038605 A038606 * A038608 A038609 A038610

Keyword

nonn,nice

Author

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

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

Status

approved