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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 Eric Weisstein's World of Mathematics, Prime Sums. The Prime Puzzles & Problems Connection: Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k. 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 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 July 9 19:46 EDT 2020. Contains 335545 sequences. (Running on oeis4.)