A233134 Prime(k), where k is such that (1 + Sum_{j=1..k} prime(j)^10) / k is an integer.

2, 3, 5, 7, 13, 19, 23, 31, 37, 41, 79, 89, 101, 103, 137, 193, 197, 223, 317, 353, 383, 457, 587, 743, 857, 997, 1049, 1117, 1279, 1321, 1693, 2213, 2423, 2887, 3079, 3271, 3797, 5011, 6701, 6833, 8443, 9901, 10429, 10691, 11059, 11731, 12253, 12841, 14221

Offset: 1

Author

Robert Price, Dec 04 2013

Keywords

• nonn

Comments

a(211) > 1005368767096627. - Bruce Garner, Jun 06 2021

Examples

			a(5) = 13, because 13 is the 6th prime and the sum of the first 6 primes^10+1 = 164088217398 when divided by 6 equals 27348036233 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..210 (first 174 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

Mathematica

t = {}; sm = 1; Do[sm = sm + Prime[n]^10; 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)^10); s==0 \\ Charles R Greathouse IV, Nov 30 2013