A233042 Prime(k), where k is such that (1 + Sum_{j=1..k} prime(j)^9) / k is an integer.

2, 3, 7, 13, 29, 37, 43, 421, 487, 3373, 5399, 6637, 7333, 117703, 124679, 130829, 218681, 243263, 374537, 2326021, 9423619, 183040409, 224628653, 255740687, 419532599, 707933033, 932059759, 2088543701, 19690779263, 27538667491, 32425948213, 51958163189, 128193738073, 1064987253349

Offset: 1

Author

Robert Price, Dec 03 2013

Keywords

• nonn

Comments

a(49) > 1005368767096627. - Bruce Garner, Jun 05 2021

Examples

			a(4) = 13, because 13 is the 6th prime and the sum of the first 6 primes^9+1 = 13004773992 when divided by 6 equals 2167462332 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..48 (first 34 terms from Robert Price)
• OEIS Wiki, Sums of powers of primes divisibility sequences

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.

Programs

Maple

A233042:=n->if type((1+add(ithprime(i)^9, i=1..n))/n, integer) then ithprime(n); fi; seq(A233042(n), n=1..100000); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

t = {}; sm = 1; Do[sm = sm + Prime[n]^9; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

PARI

is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^9); s==0 \\ Charles R Greathouse IV, Nov 30 2013