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A120480
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Primes of the form k^5 + k^2 + 1.
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4
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3, 37, 32833, 3200401, 14349637, 52523101, 130692997, 254806273, 459167941, 2706790087, 3486790963, 3939047533, 10510110703, 12762826651, 14025528757, 14693292433, 16850593873, 23863550761, 34359754753, 38579506813
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OFFSET
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1,1
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COMMENTS
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The values of k such that k^5 + k^2 + 1 is prime are 1, 2, 8, 20, 27, 35, 42, 48, 54, 77, 81, 83, 101, 105, 107, 108, 111, 119, 128, 131. Little is known about primality in quintic forms.
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LINKS
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EXAMPLE
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a(1) = 3 = 1^5 + 1^2 + 1.
a(2) = 37 = 2^5 + 2^2 + 1.
a(3) = 132833 = 8^5 + 8^2 + 1.
a(4) = 3200401 = 20^5 + 20^2 + 1.
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MATHEMATICA
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Select[Table[k^5+k^2+1, {k, 150}], PrimeQ] (* Harvey P. Dale, Oct 29 2020 *)
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PROG
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(Magma) [a: n in [0..160] | IsPrime(a) where a is n^5+n^2+1 ]; // Vincenzo Librandi, Dec 22 2010
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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