A233194 Prime(k), where k is such that (1 + Sum_{i=1..k} prime(i)^11) / k is an integer.

2, 3, 7, 11, 13, 29, 37, 59, 79, 197, 449, 1327, 3931, 197807, 504197, 1697743, 2595641, 6346793, 6986909, 8895379, 55664759, 63142507, 99624919, 129467011, 131784857, 239094833, 494415377, 951747371, 957443177, 9194035843, 52411358381, 62314028797, 69216548567, 220067593093, 3295153668199

Offset: 1

Author

Robert Price, Dec 05 2013

Keywords

• nonn

Comments

a(47) > 1005368767096627. - Bruce Garner, Jun 05 2021

Examples

			13 is a term because 13 is the 6th prime and the sum of the first 6 primes^11+1 = 2079498398712 when divided by 6 equals 346583066452 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..46
• 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]^11; 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)^11); s==0 \\ Charles R Greathouse IV, Nov 30 2013

Extensions

a(35) from Karl-Heinz Hofmann, Mar 07 2021