A233263 a(n) = prime(k), where k is such that (Sum_{j=1..k} prime(j)^12) / k is an integer.

2, 157, 72673, 52472909, 85790059, 88573873, 16903607381, 4582951241047, 162717490461611, 1220077659512857, 34871545949176799

Offset: 1

Author

Robert Price, Dec 06 2013

Keywords

• nonn
• more

Comments

a(11) > 1352363608564489. - Bruce Garner, Aug 30 2021

a(12) > 37124508045065437. - Paul W. Dyson, Jan 04 2024

Examples

			a(2) = 157, because 157 is the 37th prime and the sum of the first 37 primes^12 = 636533120636984811361212036 when divided by 37 equals 17203597855053643550303028 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

Maple

A233263:=n->if type(add(ithprime(i)^12, i=1..n)/n, integer) then ithprime(n); fi; seq(A233263(n), n=1..100000); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

t = {}; sm = 0; Do[sm = sm + Prime[n]^12; 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)^12); s==0 \\ Charles R Greathouse IV, Nov 30 2013

PARI

S=n=0;forprime(p=1,,(S+=p^12)%n++||print1(p",")) \\ M. F. Hasler, Dec 01 2013

Formula

a(n) = prime(A131272(n)).

Extensions

a(8)-a(9) from Bruce Garner, Mar 23 2021

a(10) from Bruce Garner, Aug 30 2021

a(11) from Paul W. Dyson, Jan 04 2024