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A120480 Primes of the form k^5 + k^2 + 1.

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%I A120480 #18 Sep 08 2022 08:45:26
%S A120480 3,37,32833,3200401,14349637,52523101,130692997,254806273,459167941,
%T A120480 2706790087,3486790963,3939047533,10510110703,12762826651,14025528757,
%U A120480 14693292433,16850593873,23863550761,34359754753,38579506813
%N A120480 Primes of the form k^5 + k^2 + 1.
%C A120480 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.
%H A120480 Harvey P. Dale, <a href="/A120480/b120480.txt">Table of n, a(n) for n = 1..2000</a>
%e A120480 a(1) = 3 = 1^5 + 1^2 + 1.
%e A120480 a(2) = 37 = 2^5 + 2^2 + 1.
%e A120480 a(3) = 132833 = 8^5 + 8^2 + 1.
%e A120480 a(4) = 3200401 = 20^5 + 20^2 + 1.
%t A120480 Select[Table[k^5+k^2+1,{k,150}],PrimeQ] (* _Harvey P. Dale_, Oct 29 2020 *)
%o A120480 (Magma) [a: n in [0..160] | IsPrime(a) where a is n^5+n^2+1 ]; // _Vincenzo Librandi_, Dec 22 2010
%Y A120480 Cf. A000040.
%K A120480 easy,nonn
%O A120480 1,1
%A A120480 _Jonathan Vos Post_, Jul 21 2006