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.
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).
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