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%I #39 Dec 21 2024 00:13:16
%S 2,97,277,23311,61583,6133811,210952097,359643241,5451597181,
%T 42641466149,51575229001,199655689679,248181386429,61646670874849,
%U 82153230089767,212374157550341,11432141933990629,15031011453909223
%N Prime(k), where k is such that (Sum_{j=1..k} prime(j)^11) / k is an integer.
%C a(17) > 257180056649941. - _Bruce Garner_, Mar 29 2021
%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>
%F a(n) = prime(A125827(n)).
%e a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^11 = 12718098700540100969050 when divided by 25 equals 508723948021604038762 which is an integer.
%t t = {}; sm = 0; Do[sm = sm + Prime[n]^11; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
%o (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^11); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013
%o (PARI) S=n=0;forprime(p=1,,(S+=p^11)%n++||print1(p",")) \\ _M. F. Hasler_, Dec 01 2013
%Y Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K nonn,more,changed
%O 1,1
%A _Robert Price_, Dec 05 2013
%E a(14) from _Paul W. Dyson_, Jan 08 2021
%E a(15) from _Bruce Garner_, Mar 08 2021
%E a(16) from _Bruce Garner_, Mar 29 2021
%E a(17) from _Paul W. Dyson_, Jan 03 2023
%E a(18) from _Paul W. Dyson_, Dec 20 2024