A233132 Prime(k), where k is such that (Sum_{i=1..k} prime(i)^10) / k is an integer.

2, 1723, 504017, 707602177, 3221410523, 50872396681, 502768196591, 809590307027, 7067369025727, 67826487302603, 8107773185261209, 17399114244214379

Offset: 1

Author

Robert Price, Dec 04 2013

Keywords

• nonn
• more

Comments

a(11) > 80562077557177. - Bruce Garner, Mar 06 2021

a(13) > 18205684894350047. - Paul W. Dyson, Dec 03 2024

Examples

			a(2) = 1723, because 1723 is the 269th prime and the sum of the first 269 primes^10 = 5093580907935902678630090684087692 when divided by 269 equals 18935245010914136351784723732668 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]^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

PARI

S=n=0;forprime(p=1,,(S+=p^10)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A131264(n))

Extensions

a(9)-a(10) from Bruce Garner, Mar 06 2021

a(11) from Paul W. Dyson, Jul 09 2023

a(12) from Paul W. Dyson, Dec 03 2024