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Primes of the form k^4 + 2 for k >= 0.
3

%I #26 Sep 08 2022 08:45:55

%S 2,3,83,6563,50627,194483,4100627,10556003,15752963,22667123,57289763,

%T 96059603,276922883,395254163,6059221283,6597500627,12296370323,

%U 14166950627,42110733683,44386483763,46753250627,49213429283,69257922563,72555348323

%N Primes of the form k^4 + 2 for k >= 0.

%C Apart from 3, this is a subsequence of A053786. - _Bruno Berselli_, Apr 26 2012

%H Vincenzo Librandi, <a href="/A182343/b182343.txt">Table of n, a(n) for n = 1..1000</a>

%e 2 = 0^4 + 2;

%e 3 = 1^4 + 2;

%e 83 = 3^4 + 2.

%p # choose N large, then S is the desired set

%p f:=n->n^4 + 2:

%p S:={}:

%p for n from 0 to N do if(isprime(f(n))) then S:=S union {f(n)}: fi: od:

%t Select[Range[0,600]^4 + 2,PrimeQ] (* _Bruno Berselli_, Apr 26 2012 *)

%o (Magma) [2,3] cat [n^4+2: n in [3..600 by 6]|IsPrime(n^4+2)]; // _Bruno Berselli_, Apr 26 2012

%Y Cf. A037896, A053786.

%K nonn,easy

%O 1,1

%A _Patrick Devlin_, Apr 25 2012