login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060620 Average of the first n primes rounded down. 9
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 (list; graph; refs; listen; history; text; internal format)
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.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 26 11:46 EDT 2019. Contains 322472 sequences. (Running on oeis4.)