OFFSET
1,1
COMMENTS
a(9) > 36730498487251. - Paul W. Dyson, Jan 08 2021
a(10) > 93400375993241. - Bruce Garner, Mar 17 2021
FORMULA
a(n) = prime(A131278(n)).
EXAMPLE
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.
MATHEMATICA
t = {}; sm = 0; Do[sm = sm + Prime[n]^18; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
PROG
(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
(PARI) S=n=0; forprime(p=1, , (S+=p^18)%n++||print1(p", ")) \\ - M. F. Hasler, Dec 01 2013
CROSSREFS
Cf. A085450 = smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n.
KEYWORD
nonn,more
AUTHOR
Robert Price, Dec 13 2013
EXTENSIONS
a(8) from Paul W. Dyson, Jan 08 2021
a(9) from Bruce Garner, Mar 17 2021
a(10) from Paul W. Dyson, Oct 03 2023
STATUS
approved