A038623 Smallest prime p such that p/pi(p)>=n.

2, 2, 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

Offset: 1

Author

Jud McCranie

Keywords

• nonn

Examples

			pi(37)=12 and a(3)=37 is the smallest prime >= 3*12.
		

Links

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

Crossrefs

Cf. A038624-A038627.

Essentially the same as A062743,A038607.

a(n) = prime(A038624(n)).

Programs

Mathematica

Prime[Join[{k = 1}, Table[While[Prime[k]/k < n, k++]; k, {n, 2, 18}]]] (* Jayanta Basu, Jul 10 2013 *)

PARI

k=n=1; forprime(p=2,, while(p/k>=n, print1(p", "); n++); k++) \\ Charles R Greathouse IV, Oct 15 2016

Formula

a(n) = exp(n + 1 + o(1)). - Charles R Greathouse IV, Oct 15 2016

Extensions

Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar

a(24)-a(28) from David W. Wilson, Apr 25 2017

a(29)-a(50) obtained from the values of A038625 computed by Jan Büthe. - Giovanni Resta, Sep 01 2018