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URL: https://oeis.org/A038607

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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.
7
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
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
Sequence in context: A220888 A392400 A289616 * A079009 A097651 A320540
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