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

1,1

Comments

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

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.

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007504, A090396.

Sequence in context: A125573 A034139 A238886 * A109968 A011872 A056822

Adjacent sequences: A060617 A060618 A060619 * A060621 A060622 A060623

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved