A233893 - OEIS

%I #24 Jun 05 2021 13:44:11

%S 2,3,5,7,11,13,19,23,29,37,47,53,71,89,103,113,131,167,173,197,223,

%T 271,281,409,457,463,503,541,659,787,997,1069,1279,1321,1511,2203,

%U 2297,2381,2423,3221,3331,3413,3541,4093,4327,5849,6473,8291,9851,10429,11177

%N Prime(n), where n is such that (1+sum_{i=1..n} prime(i)^4) / n is an integer.

%C a(280) > 1701962315686097. - _Bruce Garner_, Jun 05 2021

%H Bruce Garner, <a href="/A233893/b233893.txt">Table of n, a(n) for n = 1..279</a> (terms 1..215 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(6) = 13, because 13 is the 6th prime and the sum of the first 6 primes^4+1 = 46326 when divided by 6 equals 7721 which is an integer.

%t t = {}; sm = 1; Do[sm = sm + Prime[n]^4; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)

%t Module[{nn=1400,t},t=Accumulate[Prime[Range[nn]]^4]+1;Prime[#]&/@ Transpose[Select[Thread[{Range[nn],t}],IntegerQ[#[[2]]/#[[1]]]&]][[1]]](* _Harvey P. Dale_, Sep 06 2015 *)

%o (PARI) is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^4); 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 17 2013