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A171399 Prime(n), where n is such that (sum_{i=1..n} prime(i)) / n is an integer. 92
2, 83, 241, 6599, 126551, 1544479, 4864121, 60686737, 1966194317, 63481708607, 1161468891953, 14674403807731, 22128836547913 (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(n) = A000040(A045345(n)).

a(13) > 2*10^13. - Donovan Johnson, Aug 23 2010

LINKS

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

Kaisa Matomäki, A note on the sum of the first n primes, Quart. J. Math. 61 (2010), pp. 109-115.

OEIS Wiki, Sums of powers of primes divisibility sequences

EXAMPLE

a(3) = 83, because 83 is 23rd prime and (sum_(i=1...23) p_i) / 23 = 874 / 23 = 38 (integer).

MAPLE

with(numtheory);

P:=proc(i)

local n, s; s:=0;

for n from 1 to i do

   s:=s+ithprime(n);

   if s/n=trunc(s/n) then print(ithprime(n)); fi;

od; end: # Paolo P. Lava, Feb 10 2012.

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.

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

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

Sequence in context: A007353 A108312 A175449 * A037069 A065591 A266201

Adjacent sequences:  A171396 A171397 A171398 * A171400 A171401 A171402

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

STATUS

approved

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Last modified November 21 12:20 EST 2019. Contains 329370 sequences. (Running on oeis4.)