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A171399 Prime(k), where k is such that (Sum_{i=1..k} prime(i)) / k is an integer. 94
2, 83, 241, 6599, 126551, 1544479, 4864121, 60686737, 1966194317, 63481708607, 1161468891953, 14674403807731, 22128836547913, 399379081448429, 5410229663058299, 248264241666057167 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Corresponding values of k, Sum_{i=1..k} p_i, and (Sum_{i=1..k} p_i) / k are given in A045345, A050247 and A050248. No other solutions for p_k < 4011201392413.
a(13) > 2*10^13. - Donovan Johnson, Aug 23 2010
a(16) > 5456843462009647. - Bruce Garner, Mar 06 2021
a(17) > 253814097223614463. - Paul W. Dyson, Sep 26 2022
LINKS
Kaisa Matomäki, A note on the sum of the first n primes, Quart. J. Math. 61 (2010), pp. 109-115.
FORMULA
a(n) = A000040(A045345(n)).
EXAMPLE
83 is the 23rd prime and (Sum_{i=1..23} p_i) / 23 = 874 / 23 = 38 (integer), so 83 is a term.
MATHEMATICA
t = {}; sm = 0; Do[sm = sm + Prime[n]; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* T. D. Noe, Mar 19 2013 *)
PROG
(PARI) s=0; n=0; forprime(p=2, 1e7, s+=p; if(s%n++==0, print1(p", "))) \\ Charles R Greathouse IV, Jun 13 2012
CROSSREFS
Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
Sequence in context: A108312 A175449 A371475 * A037069 A065591 A266201
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Dec 07 2009
EXTENSIONS
a(6) corrected and a(12) from Donovan Johnson, Aug 23 2010
a(13) from Robert Price, Mar 17 2013
a(14)-a(15) from Bruce Garner, Mar 06 2021
a(16) from Paul W. Dyson, Sep 26 2022
STATUS
approved

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Last modified April 20 06:42 EDT 2024. Contains 371799 sequences. (Running on oeis4.)