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A317979 Numbers k such that k^4 + k^3 + k^2 + 1 is prime.

%I A317979 #29 Sep 08 2022 08:46:22
%S A317979 2,4,6,8,14,22,26,32,36,54,82,96,98,108,116,120,124,132,144,152,162,
%T A317979 164,166,182,226,240,244,246,252,254,264,266,274,276,312,314,322,328,
%U A317979 330,352,364,368,372,382,406,410,420,422,428,430,432,438,456
%N A317979 Numbers k such that k^4 + k^3 + k^2 + 1 is prime.
%C A317979 The numbers in the sequence are all even numbers.
%C A317979 For k = 11*m - 4, (k^4 + k^3 + k^2 + 1)/11 is an integer, so there is no number of the form k = 11*m - 4 in the sequence.
%H A317979 Daniel Starodubtsev, <a href="/A317979/b317979.txt">Table of n, a(n) for n = 1..10000</a>
%e A317979 2^4 + 2^3 + 2^2 + 1 = 29 is prime, so 2 is in the sequence.
%t A317979 Select[Range[0, 1000], PrimeQ[#^4 + #^3 + #^2 + 1] &]
%o A317979 (PARI) for(n=1, 1000, if(ispseudoprime(n^4 + n^3 + n^2 + 1), print1(n, ", ")))
%o A317979 (Magma) [n: n in [0..700] |IsPrime(n^4 + n^3 + n^2 + 1)]; // _Vincenzo Librandi_, Sep 08 2018
%Y A317979 Cf. A005574, A119863.
%K A317979 nonn
%O A317979 1,1
%A A317979 _Jinyuan Wang_, Aug 12 2018