A233350 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^13) / k is an integer.

2, 3, 7, 13, 29, 37, 239, 373, 769, 1531, 2011, 5003, 11939, 14557, 14629, 37361, 204361, 252431, 289193, 1403189, 2201623, 2299541, 6287173, 6734179, 29155393, 29235133, 103558313, 186122161, 531627839, 623579347, 4245274987, 6718076401, 16495027789, 39151049879, 90009559583, 225919038109

Offset: 1

Author

Robert Price, Dec 07 2013

Keywords

• nonn

Comments

a(47) > 458158058915101. - Bruce Garner, May 05 2021

Examples

			a(4) = 13, because 13 is the 6th prime and the sum of the first 6 primes^13+1 = 337495930052232 when divided by 6 equals 56249321675372 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..46
• OEIS Wiki, Sums of powers of primes divisibility sequences

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.

Programs

Mathematica

t = {}; sm = 1; Do[sm = sm + Prime[n]^13; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

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