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A232963
Prime(m), where m is such that (sum_{i=1..m} prime(i)^14) / m is an integer.
0
2, 1933, 3217, 41681, 114311, 2743691233, 7252463461, 28682755720447, 2839633449523319
OFFSET
1,1
COMMENTS
a(8) > 1093881323023.
The primes correspond to indices n = 1, 295, 455, 4361, 10817, 132680789, 334931875, 957643538339 = A131274.
a(9) > 30377067936647. - Paul W. Dyson, Jan 03 2021
FORMULA
a(n) = prime(A131274(n)).
EXAMPLE
a(2) = 1933, because 1193391 is the 295th prime and the sum of the first 295 primes^14 = 172657243368537051859007103457435197295421033550 when divided by 295 equals 585278791079786616471210520194695584052274690 which is an integer.
MATHEMATICA
t = {}; sm = 0; Do[sm = sm + Prime[n]^14; 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)^14); s==0 \\ Charles R Greathouse IV, Nov 30 2013
(PARI) S=n=0; forprime(p=1, , (S+=p^14)%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: A230082 A217372 A160299 * A238119 A177188 A125635
KEYWORD
nonn,more
AUTHOR
Robert Price, Dec 02 2013
EXTENSIONS
a(8) from Paul W. Dyson, Jan 03 2021
a(9) from Bruce Garner, Mar 28 2022
STATUS
approved