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 A232770 Prime(k), where k is such that (Sum_{i=1..k} prime(i)^13) / k is an integer. 0
 2, 83, 1979, 2081, 2326469, 6356923, 7170679, 63812027, 4652001719, 241949473277, 163220642765623, 1260677492111911 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(13) > 1352363608564489. - Bruce Garner, Aug 30 2021 LINKS EXAMPLE a(2) = 83, because 83 is the 23rd prime and the sum of the first 23 primes^13 = 17226586990098074754709144 when divided by 23 equals 748982043047742380639528 which is an integer. MATHEMATICA t = {}; sm = 0; Do[sm = sm + Prime[n]^13; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *) PROG (PARI) is(n)=if(!isprime(n), return(0)); my(t=primepi(n), s); forprime(p=2, n, s+=Mod(p, t)^13); s==0 \\ Charles R Greathouse IV, Nov 30 2013 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: A065591 A266201 A225807 * A317724 A099373 A169601 Adjacent sequences:  A232767 A232768 A232769 * A232771 A232772 A232773 KEYWORD nonn,more AUTHOR Robert Price, Nov 29 2013 EXTENSIONS a(11) from Bruce Garner, Mar 23 2021 a(12) from Bruce Garner, Aug 30 2021 STATUS approved

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Last modified January 22 19:45 EST 2022. Contains 350504 sequences. (Running on oeis4.)