A064658 a(n) = ceiling(prime(n) - n*log(n)).

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, 12, 11, 21, 21, 22, 20, 25, 22, 24, 25, 25, 26, 27, 25, 30, 27, 26, 23, 31, 38, 37, 34, 33, 34, 31, 36, 37, 38, 39, 36, 37, 36, 33, 38, 46, 45, 42, 41, 50, 51, 55

Offset: 1

Author

N. J. A. Sloane, Oct 10 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Vaclav Kotesovec, 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

Crossrefs

Cf. A064659, A059111.

Programs

Mathematica

Table[Ceiling[Prime[n]-n Log[n]],{n,70}] (* Harvey P. Dale, Dec 07 2018 *)

PARI

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

Formula

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

Extensions

Definition corrected by Harry J. Smith, Jun 24 2009