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%I #13 Sep 08 2022 08:45:25
%S 3,739,2986129,11390851,191103553,387421219,1291469059,2176783633,
%T 8303767651,24794914213,34296450499,646990192099,782757798913,
%U 2194972636933,3462826006819,14412774469393,27752076894853
%N Primes of the form k^6 + k^2 + 1.
%C The numbers k such that k^6 + k^2 + 1 is prime begin 1, 3, 12, 15, 24, 27, 33, 36, 45, 54, 57, 93, 96, 114, 123, 156, 174, 177, 210, ...; other than 1, each is divisible by 3.
%F a(n) = A000040 INTERSECTION {n^6 + n^2 + 1}.
%e a(1) = 1^6 + 1^2 + 1 = 3 is prime.
%e a(2) = 3^6 + 3^2 + 1 = 739 is prime.
%e a(3) = 12^6 + 12^2 + 1 = 2986129 is prime.
%e a(4) = 15^6 + 15^2 + 1 = 11390851 is prime.
%t Select[Table[n^6+n^2+1,{n,200}],PrimeQ] (* _Harvey P. Dale_, Oct 17 2019 *)
%o (Magma) [a: n in [0..250]|IsPrime(a) where a is n^6+n^2+1] // _Vincenzo Librandi_, Dec 22 2010
%Y Cf. A000040, A120479, A120480.
%K easy,nonn,less
%O 1,1
%A _Jonathan Vos Post_, Jul 23 2006
%E a(1) corrected by _Vincenzo Librandi_, Dec 22 2010
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