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A119264
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Primes of the form k^6 + k^2 + 1.
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2
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3, 739, 2986129, 11390851, 191103553, 387421219, 1291469059, 2176783633, 8303767651, 24794914213, 34296450499, 646990192099, 782757798913, 2194972636933, 3462826006819, 14412774469393, 27752076894853
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = A000040 INTERSECTION {n^6 + n^2 + 1}.
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EXAMPLE
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a(1) = 1^6 + 1^2 + 1 = 3 is prime.
a(2) = 3^6 + 3^2 + 1 = 739 is prime.
a(3) = 12^6 + 12^2 + 1 = 2986129 is prime.
a(4) = 15^6 + 15^2 + 1 = 11390851 is prime.
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MATHEMATICA
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Select[Table[n^6+n^2+1, {n, 200}], PrimeQ] (* Harvey P. Dale, Oct 17 2019 *)
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PROG
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(Magma) [a: n in [0..250]|IsPrime(a) where a is n^6+n^2+1] // Vincenzo Librandi, Dec 22 2010
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CROSSREFS
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KEYWORD
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easy,nonn,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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