A232824 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^8) / k is an integer.

2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 47, 53, 71, 89, 107, 113, 131, 157, 167, 173, 197, 223, 281, 311, 409, 463, 503, 541, 569, 659, 751, 941, 997, 1033, 1069, 1259, 1297, 1511, 1567, 2129, 2423, 3221, 3413, 3671, 3907, 4057, 4091, 4231, 5051, 5197, 5569

Offset

1,1

Comments

a(305) > 4193009611262897. - Bruce Garner, Mar 20 2022

Links

Bruce Garner, Table of n, a(n) for n = 1..304 (terms 1..227 from Robert Price)

OEIS Wiki, Sums of powers of primes divisibility sequences

Example

a(5) = 11, because 11 is the 5th prime and the sum of the first 5 primes^8+1 = 220521125 when divided by 5 equals 44104225 which is an integer.

Mathematica

t = {}; sm = 1; Do[sm = sm + Prime[n]^8; 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)^8); s==0 \\ Charles R Greathouse IV, Nov 30 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: A106639 A233462 A233893 * A078334 A108696 A215642

Adjacent sequences: A232821 A232822 A232823 * A232825 A232826 A232827

Keyword

nonn

Author

Robert Price, Nov 30 2013

Status

approved