This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A233350 #21 May 05 2021 18:12:09
%S A233350 2,3,7,13,29,37,239,373,769,1531,2011,5003,11939,14557,14629,37361,
%T A233350 204361,252431,289193,1403189,2201623,2299541,6287173,6734179,
%U A233350 29155393,29235133,103558313,186122161,531627839,623579347,4245274987,6718076401,16495027789,39151049879,90009559583,225919038109
%N A233350 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^13) / k is an integer.
%C A233350 a(47) > 458158058915101. - _Bruce Garner_, May 05 2021
%H A233350 Bruce Garner, <a href="/A233350/b233350.txt">Table of n, a(n) for n = 1..46</a>
%H A233350 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%e A233350 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.
%t A233350 t = {}; sm = 1; Do[sm = sm + Prime[n]^13; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o A233350 (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
%Y A233350 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A233350 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A233350 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A233350 nonn
%O A233350 1,1
%A A233350 _Robert Price_, Dec 07 2013