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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.

%I A038607 #24 Oct 04 2022 21:21:56
%S A038607 2,11,37,127,347,1087,3109,8419,24317,64553,175211,480881,1304707,
%T A038607 3523901,9558533,25874843,70115473,189961529,514272533,1394193607,
%U A038607 3779851091,10246935679,27788566133,75370121191,204475052401,554805820711,1505578023841,4086199302113,11091501631019,30109570413007
%N A038607 a(n) is the smallest prime number k such that k > n*pi(k), where pi(k) denotes the prime counting function.
%C A038607 a(n) is about exp(n+1+1/(n+1)). - _Charles R Greathouse IV_, Sep 05 2011
%H A038607 Giovanni Resta, <a href="/A038607/b038607.txt">Table of n, a(n) for n = 1..50</a>
%F A038607 a(n) = prime(A038606(n)) = A000040(A038606(n)).
%e A038607 For n=1, a(1) = 2, since 2 > 1*pi(2) = 1*1. - _N. J. A. Sloane_, Dec 09 2020
%e A038607 For n=3, the 12th prime (37) is the first one satisfying p(k) > 3k.
%t A038607 k = 1; Do[ While[ Prime[k] < n*k, k++ ]; Print[Prime[k]], {n, 1, 25} ]
%o A038607 (PARI) k=1;n=1;forprime(p=3,4e9,if(p/n++>k,print1(p", ");k++)) \\ _Charles R Greathouse IV_, Sep 06 2011
%Y A038607 Cf. A038606, A038623.
%K A038607 nonn,nice
%O A038607 1,1
%A A038607 Vasiliy Danilov (danilovv(AT)usa.net), Jul 1998
%E A038607 Extended by _Robert G. Wilson v_ and _Ray Chandler_, Dec 01 2004
%E A038607 a(26)-a(30) from _Charles R Greathouse IV_, Sep 05 2011, Sep 06 2011
%E A038607 a(31)-a(50) obtained from the values of A038625 computed by _Jan Büthe_. - _Giovanni Resta_, Sep 01 2018