A059112 floor(prime(n) - n*log(n) - n*log(log(n)) + n).

4, 4, 4, 5, 4, 5, 4, 5, 7, 6, 8, 8, 6, 6, 8, 10, 7, 9, 9, 6, 8, 7, 8, 12, 11, 8, 7, 5, 4, 13, 12, 13, 10, 15, 12, 12, 13, 12, 13, 13, 10, 15, 11, 10, 7, 13, 20, 18, 15, 13, 14, 10, 14, 15, 15, 15, 12, 12, 10, 7, 11, 19, 17, 13, 11, 20, 20, 24, 20, 18, 18, 20, 20, 20, 18, 18, 20, 18

Offset: 2

Author

Henry Bottomley, Jan 04 2001

Keywords

• nonn
• easy

Examples

			a(10000) = floor[104729 - 92103.403 - 22203.268 + 10000] = floor[422.328] = 422.
		

Links

• C. K. Caldwell, How Many Primes Are There?

Crossrefs

Cf. A000040, A059111.

Programs

Mathematica

Table[Floor[Prime[n]-n Log[n]-n Log[Log[n]]+n],{n,2,80}] (* Harvey P. Dale, Jul 10 2023 *)

PARI

vector(100,n,floor(prime(n+1) - (n+1)*log(n+1) - (n+1)*log(log(n+1))+n+1)) \\ Derek Orr, Oct 27 2014