A233192 Prime(k), where k is such that (Sum_{j=1..k} prime(j)^11) / k is an integer.

2, 97, 277, 23311, 61583, 6133811, 210952097, 359643241, 5451597181, 42641466149, 51575229001, 199655689679, 248181386429, 61646670874849, 82153230089767, 212374157550341, 11432141933990629, 15031011453909223

Offset

1,1

Comments

a(17) > 257180056649941. - Bruce Garner, Mar 29 2021

Links

Table of n, a(n) for n=1..18.

OEIS Wiki, Sums of powers of primes divisibility sequences

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.

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A297423 A189313 A042151 * A065592 A233767 A223936

Adjacent sequences: A233189 A233190 A233191 * A233193 A233194 A233195

Keyword

nonn,more,changed

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

a(18) from Paul W. Dyson, Dec 20 2024

Status

approved