A064658 - OEIS

%I #14 May 23 2020 02:23:29

%S 2,2,2,2,3,3,4,3,4,6,5,8,8,7,7,9,11,9,12,12,10,11,11,13,17,17,15,14,

%T 12,11,21,21,22,20,25,22,24,25,25,26,27,25,30,27,26,23,31,38,37,34,33,

%U 34,31,36,37,38,39,36,37,36,33,38,46,45,42,41,50,51,55

%N a(n) = ceiling(prime(n) - n*log(n)).

%H Harry J. Smith, <a href="/A064658/b064658.txt">Table of n, a(n) for n = 1..1000</a>

%H Vaclav Kotesovec, <a href="/A064658/a064658.jpg">Plot of a(n) / (n*log(log(n)) * (1 + 1/log(n) - 1/log(log(n)) - 2/(log(n)*log(log(n))))) for n = 2..100000</a>

%F a(n) ~ n*log(log(n)) * (1 + 1/log(n) - 1/log(log(n)) - 2/(log(n)*log(log(n)))). - _Vaclav Kotesovec_, May 23 2020

%t Table[Ceiling[Prime[n]-n Log[n]],{n,70}] (* _Harvey P. Dale_, Dec 07 2018 *)

%o (PARI) { default(realprecision, 100); for (n = 1, 1000, write("b064658.txt", n, " ", ceil(prime(n) - n*log(n))); ) } \\ _Harry J. Smith_, Jun 25 2009

%Y Cf. A064659, A059111.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Oct 10 2001

%E Definition corrected by _Harry J. Smith_, Jun 24 2009