A233575 - OEIS

%I #25 Dec 17 2024 00:50:37

%S 2,157,1697,190573,167719729,22092660553,57613776809,4386989244577,

%T 91982826261331,13432259712845291

%N Prime(m), where m is such that (Sum_{i=1..m} prime(i)^18) / m is an integer.

%C a(9) > 36730498487251. - _Paul W. Dyson_, Jan 08 2021

%C a(10) > 93400375993241. - _Bruce Garner_, Mar 17 2021

%C a(11) > 18205684894350047. - _Paul W. Dyson_, Dec 16 2024

%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(A131278(n)).

%e a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^18 = 7222759943091280921446062146835136523956 when divided by 37 equals 195209728191656241120163841806355041188 which is an integer.

%t t = {}; sm = 0; Do[sm = sm + Prime[n]^18; 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)^18); s==0 \\ _Charles R Greathouse IV_, Nov 30 2013

%o (PARI) S=n=0;forprime(p=1,,(S+=p^18)%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

%O 1,1

%A _Robert Price_, Dec 13 2013

%E a(8) from _Paul W. Dyson_, Jan 08 2021

%E a(9) from _Bruce Garner_, Mar 17 2021

%E a(10) from _Paul W. Dyson_, Oct 03 2023