A233192 Prime(k), where k is such that (Sum_{j=1..k} prime(j)^11) / k is an integer.

2, 97, 277, 23311, 61583, 6133811, 210952097, 359643241, 5451597181, 42641466149, 51575229001, 199655689679, 248181386429, 61646670874849, 82153230089767, 212374157550341, 11432141933990629, 15031011453909223

Offset: 1

Author

Robert Price, Dec 05 2013

Keywords

• nonn
• more

Comments

a(17) > 257180056649941. - Bruce Garner, Mar 29 2021

a(19) > 18205684894350047. - Paul W. Dyson, Jan 16 2025

Examples

			a(2) = 97, because 97 is the 25th prime and the sum of the first 25 primes^11 = 12718098700540100969050 when divided by 25 equals 508723948021604038762 which is an integer.
		

Links

• 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 = 0; 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

PARI

S=n=0;forprime(p=1,,(S+=p^11)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A125827(n)).

Extensions

a(14) from Paul W. Dyson, Jan 08 2021

a(15) from Bruce Garner, Mar 08 2021

a(16) from Bruce Garner, Mar 29 2021

a(17) from Paul W. Dyson, Jan 03 2023

a(18) from Paul W. Dyson, Dec 20 2024