A060620 Average of the first n primes rounded down.

2, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 33, 35, 38, 40, 42, 44, 46, 48, 51, 53, 55, 57, 60, 62, 65, 67, 69, 72, 74, 77, 79, 82, 84, 87, 89, 91, 94, 97, 99, 102, 104, 107, 110, 112, 115, 117, 120, 123, 125, 128, 130, 133, 136, 138, 141, 144

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 25 2001

Keywords

• nonn
• easy

Comments

Closely related to the prime number theorem; a(n) has the asymptotic expression n * log(n) / 2.

Examples

			a(5) = floor((2 + 3 + 5 + 7 + 11)/5) = 5.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Romeo Meštrović, Curious conjectures on the distribution of primes among the sums of the first 2n primes, arXiv:1804.04198 [math.NT], 2018.

Crossrefs

Cf. A007504, A090396.

Programs

Mathematica

With[{prms=Prime[Range[500]]},Table[Floor[Mean[Take[prms,n]]],{n,70}]]  (* Harvey P. Dale, Mar 09 2011 *)

PARI

{ n=0; s=0; forprime (p=2, prime(1000), s+=p; write("b060620.txt", n++, " ", floor(s/n)); ) } \\ Harry J. Smith, Jul 08 2009

PARI

a(n) = sum(k=1, n, prime(k))\n; \\ Michel Marcus, Jul 03 2018

Formula

a(n) = floor(A007504(n) / n).

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2001