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A038607 a(n) is the smallest prime number k such that k > n*pi(k), where pi(k) denotes the prime counting function. 5
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 (list; graph; refs; listen; history; text; internal format)
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=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) 1998 Jul

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

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)