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a(n) = floor(prime(n) - n*log(n)).
8

%I #15 Sep 08 2022 08:45:02

%S 2,1,1,1,2,2,3,2,3,5,4,7,7,6,6,8,10,8,11,11,9,10,10,12,16,16,14,13,11,

%T 10,20,20,21,19,24,21,23,24,24,25,26,24,29,26,25,22,30,37,36,33,32,33,

%U 30,35,36,37,38,35,36,35,32,37,45,44,41,40,49,50,54,51,50,51,53,54,55

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

%H Harry J. Smith, <a href="/A059111/b059111.txt">Table of n, a(n) for n = 1..1000</a>

%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/howmany.shtml">How Many Primes Are There?</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFormulas.html">Prime formulas</a>

%t Table[Floor[Prime[n]-n Log[n]],{n,100}] (* _Harvey P. Dale_, May 02 2011 *)

%o (PARI) { default(realprecision, 100); for (n = 1, 1000, write("b059111.txt", n, " ", floor(prime(n) - n*log(n))); ) } \\ _Harry J. Smith_, Jun 25 2009

%o (Magma) [ Floor(NthPrime(n)-n*Log(n)): n in [1..75] ]; // _Bruno Berselli_, May 02 2011

%Y Cf. A064658, A064659, A059112.

%K nonn

%O 1,1

%A _Henry Bottomley_, Jan 04 2001

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