A204594 Nearest integer to n*log(n) + n*log(log(n)) - n + n/log(n)*(log(log(n))-2) - n*log(log(n))*(log(log(n))-6)/(2 log(n)^2), an asymptotic expression for prime(n).

-13, -4, 0, 3, 6, 10, 13, 17, 20, 24, 28, 32, 36, 40, 44, 49, 53, 57, 62, 66, 71, 76, 80, 85, 90, 95, 100, 105, 109, 115, 120, 125, 130, 135, 140, 145, 151, 156, 161, 167, 172, 177, 183, 188, 194, 199, 205, 210, 216, 222, 227, 233, 239, 244, 250, 256, 262

Offset: 2

Author

M. F. Hasler, Feb 07 2012

Keywords

• sign

Links

• Pierre Dusart, Estimates of Some Functions Over Primes without R.H. (2010).
• Wikipedia, Prime number theorem

Crossrefs

Cf. A059112, A059111, A064658, A064659.

Programs

Mathematica

Table[Round[n Log[n] + n Log[Log[n]] - n + n/Log[n](Log[Log[n]] - 2) - n Log[Log[n]](Log[Log[n]] - 6)/(2 Log[n]^2)], {n, 2, 58}] (* Alonso del Arte, Feb 07 2012 *)

PARI

A204594(n)=round(n*log(n)+n*log(log(n))-n+n/log(n)*(log(log(n))-2)-n*log(log(n))/2/log(n)^2*(log(log(n))-6))