A232770 Prime(k), where k is such that (Sum_{i=1..k} prime(i)^13) / k is an integer.

2, 83, 1979, 2081, 2326469, 6356923, 7170679, 63812027, 4652001719, 241949473277, 163220642765623, 1260677492111911, 8150959175977039

Offset

1,1

Comments

a(13) > 1352363608564489. - Bruce Garner, Aug 30 2021

a(14) > 18205684894350047. - Paul W. Dyson, Dec 06 2024

Links

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

OEIS Wiki, Sums of powers of primes divisibility sequences

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

a(13) from Paul W. Dyson, Apr 20 2023

Status

approved