OFFSET
1,1
COMMENTS
a(11) > 80562077557177. - Bruce Garner, Mar 06 2021
a(13) > 18205684894350047. - Paul W. Dyson, Dec 03 2024
FORMULA
a(n) = prime(A131264(n))
EXAMPLE
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.
MATHEMATICA
t = {}; sm = 0; Do[sm = sm + Prime[n]^10; 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)^10); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) S=n=0; forprime(p=1, , (S+=p^10)%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 04 2013
EXTENSIONS
a(9)-a(10) from Bruce Garner, Mar 06 2021
a(11) from Paul W. Dyson, Jul 09 2023
a(12) from Paul W. Dyson, Dec 03 2024
STATUS
approved