A233134 - OEIS

%I #22 Jun 06 2021 06:42:20

%S 2,3,5,7,13,19,23,31,37,41,79,89,101,103,137,193,197,223,317,353,383,

%T 457,587,743,857,997,1049,1117,1279,1321,1693,2213,2423,2887,3079,

%U 3271,3797,5011,6701,6833,8443,9901,10429,10691,11059,11731,12253,12841,14221

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

%C a(211) > 1005368767096627. - _Bruce Garner_, Jun 06 2021

%H Bruce Garner, <a href="/A233134/b233134.txt">Table of n, a(n) for n = 1..210</a> (first 174 terms from Robert Price)

%H OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>

%e 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.

%t t = {}; sm = 1; Do[sm = sm + Prime[n]^10; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

%o (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

%Y Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

%Y Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

%Y Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

%K nonn

%O 1,1

%A _Robert Price_, Dec 04 2013