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A233192
Prime(k), where k is such that (Sum_{j=1..k} prime(j)^11) / k is an integer.
0
2, 97, 277, 23311, 61583, 6133811, 210952097, 359643241, 5451597181, 42641466149, 51575229001, 199655689679, 248181386429, 61646670874849, 82153230089767, 212374157550341, 11432141933990629
OFFSET
1,1
COMMENTS
a(17) > 257180056649941. - Bruce Garner, Mar 29 2021
FORMULA
a(n) = prime(A125827(n)).
EXAMPLE
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.
MATHEMATICA
t = {}; sm = 0; Do[sm = sm + Prime[n]^11; 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)^11); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) S=n=0; forprime(p=1, , (S+=p^11)%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.
Sequence in context: A297423 A189313 A042151 * A065592 A233767 A223936
KEYWORD
nonn,more
AUTHOR
Robert Price, Dec 05 2013
EXTENSIONS
a(14) from Paul W. Dyson, Jan 08 2021
a(15) from Bruce Garner, Mar 08 2021
a(16) from Bruce Garner, Mar 29 2021
a(17) from Paul W. Dyson, Jan 03 2023
STATUS
approved