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A050248 Integer averages of first n primes for some n. 103
2, 38, 110, 3066, 60020, 740282, 2340038, 29380602, 957565746, 31043311588, 569424748566, 7207204117608, 10871205353578 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(10) and a(11) were found by Giovanni Resta (Nov 15 2004). He states that there are no other terms for primes p < 4011201392413. See link to Prime Puzzles, Puzzle 31 below.

a(13) > (sum of first pi(2*10^13) primes)/pi(2*10^13). - Donovan Johnson, Aug 23 2010

LINKS

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Prime Sums.

The Prime Puzzles & Problems Connection: Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k.

OEIS Wiki, Sums of powers of primes divisibility sequences

FORMULA

a(n) = A050247(n)/A045345(n).

EXAMPLE

38 is average of first n = 23 primes; 110 (n = 53); 3066 (n = 853); 60020 (n = 11869).

MATHEMATICA

a=0; lst={}; Do[p=Prime[n]; a+=p; If[a/n==IntegerPart[a/n], AppendTo[lst, a/n]], {n, 10!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 05 2009 *)

PROG

(PARI) s=n=0; forprime(p=2, 1e9, if((s+=p)%n++==0, print1(s/n", "))) \\ Charles R Greathouse IV, Nov 07 2014

CROSSREFS

Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A173026 A294396 A075459 * A105645 A098456 A214909

Adjacent sequences:  A050245 A050246 A050247 * A050249 A050250 A050251

KEYWORD

nonn,more

AUTHOR

Eric W. Weisstein

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of David W. Wilson, Jun 23 2007

a(10)-a(11) from Giovanni Resta via Ray Chandler, Jul 19 2010

a(12) from Donovan Johnson, Aug 23 2010

a(13) from Robert Price, Mar 17 2013

STATUS

approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)