A232963 Prime(m), where m is such that (sum_{i=1..m} prime(i)^14) / m is an integer.

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

Links

Table of n, a(n) for n=1..9.

OEIS Wiki, Sums of powers of primes divisibility sequences

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.

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

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

Sequence in context: A230082 A217372 A160299 * A238119 A177188 A125635

Adjacent sequences: A232960 A232961 A232962 * A232964 A232965 A232966

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