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A204325 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)). 0
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, 12, 9, 14, 10, 11, 12, 11, 11, 12, 9, 13, 10, 8, 5, 11, 18, 16, 12, 11, 11, 8, 12, 12, 12, 13, 9, 9, 7, 4, 8, 16, 14, 10, 8, 16, 16, 20, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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))

REFERENCES

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.

LINKS

Table of n, a(n) for n=2..70.

Pierre Dusart, Estimates of Some Functions Over Primes without R.H. (2010).

Wikipedia, Prime number theorem

MATHEMATICA

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}]

CROSSREFS

Cf. A064658, A059111.

Sequence in context: A028579 A007263 A033336 * A102270 A102272 A304227

Adjacent sequences:  A204322 A204323 A204324 * A204326 A204327 A204328

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Jan 14 2012

STATUS

approved

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Last modified April 5 16:24 EDT 2020. Contains 333245 sequences. (Running on oeis4.)