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%I #30 Mar 31 2012 10:26:26
%S 16,8,7,7,6,7,5,6,8,6,9,9,7,6,8,10,8,9,9,6,8,7,8,11,11,8,7,4,3,12,11,
%T 12,9,14,10,11,12,11,11,12,9,13,10,8,5,11,18,16,12,11,11,8,12,12,12,
%U 13,9,9,7,4,8,16,14,10,8,16,16,20,16
%N Residual of an asymptotic formula for the n-th prime: Floor(prime(n)-n*log(n) + n - n*log(log(n)) - (n/log(n))*(log(log(n)) - 2) + (log(log(n)) - 6)*n*log(log(n))/(2*log(n)^2)).
%C prime(n) ~ n*log(n)+n-n*log(log(n)) - (n/log(n))*(log(log(n))-2)+(log(log(n))-6)*n*log(log(n))/(2*log(n)^2))
%D M. Cipolla, "La determinazione asintotica dell'n-mo numero primo.", Rend. d. R. Acc. di sc. fis. e mat. di Napoli, s. 3, VIII (1902), pp. 132-166.
%H Pierre Dusart, <a href="http://arxiv.org/abs/1002.0442">Estimates of Some Functions Over Primes without R.H.</a> (2010).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_number_theorem">Prime number theorem</a>
%t Table[Floor[Prime[n]-n*Log[n]+n-n*Log[Log[n]]- (n/Log[n]) (Log[Log[n]]-2)+(Log[Log[n]]-6)*n*Log[Log[n]]/(2*Log[n]^2)],{n,2,100}]
%Y Cf. A064658, A059111.
%K nonn
%O 2,1
%A _José María Grau Ribas_, Jan 14 2012
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