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A050248
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Integer averages of first n primes for some n.
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12
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2, 38, 110, 3066, 60020, 740282, 2340038, 29380602, 957565746, 31043311588, 569424748566, 7207204117608
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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). [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 23 2010]
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
The Prime Puzzles & Problems Connection: Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k.
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EXAMPLE
| 38 is average of first n=23 primes; 110 (n=53); 3066 (n=853); 60020(n=11869).
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MATHEMATICA
| a=0; lst={}; Do[p=Prime[n]; a+=p; If[a/n==IntegerPart[a/n], AppendTo[lst, a/n]], {n, 10!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 05 2009]
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CROSSREFS
| a(n) = A050247/A045345.
Sequence in context: A068401 A173026 A075459 * A105645 A098456 A179503
Adjacent sequences: A050245 A050246 A050247 * A050249 A050250 A050251
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KEYWORD
| nonn,more
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of David W. Wilson, Jun 23 2007
a(10), a(11) from Giovanni Resta submitted by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 19 2010
a(12) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 23 2010
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