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 A233132 #25 Dec 03 2024 04:21:45
%S A233132 2,1723,504017,707602177,3221410523,50872396681,502768196591,
%T A233132 809590307027,7067369025727,67826487302603,8107773185261209,
%U A233132 17399114244214379
%N A233132 Prime(k), where k is such that (Sum_{i=1..k} prime(i)^10) / k is an integer.
%C A233132 a(11) > 80562077557177. - _Bruce Garner_, Mar 06 2021
%C A233132 a(13) > 18205684894350047. - _Paul W. Dyson_, Dec 03 2024
%H A233132 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%F A233132 a(n) = prime(A131264(n))
%e A233132 a(2) = 1723, because 1723 is the 269th prime and the sum of the first 269 primes^10 = 5093580907935902678630090684087692 when divided by 269 equals 18935245010914136351784723732668 which is an integer.
%t A233132 t = {}; sm = 0; Do[sm = sm + Prime[n]^10; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o A233132 (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^10); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%o A233132 (PARI) S=n=0;forprime(p=1,,(S+=p^10)%n++||print1(p",")) \\ _M. F. Hasler_, Dec 01 2013
%Y A233132 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A233132 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A233132 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A233132 nonn,more
%O A233132 1,1
%A A233132 _Robert Price_, Dec 04 2013
%E A233132 a(9)-a(10) from _Bruce Garner_, Mar 06 2021
%E A233132 a(11) from _Paul W. Dyson_, Jul 09 2023
%E A233132 a(12) from _Paul W. Dyson_, Dec 03 2024