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%I #16 Sep 08 2022 08:44:58
%S 1,2,5,6,9,11,12,14,24,26,32,36,44,47,60,69,72,74,77,89,90,102,107,
%T 119,126,131,146,147,159,162,170,171,186,191,197,204,206,219,239,240,
%U 252,266,284,285,290,296,300,324,347,351,362,384,426,437,459,465,470
%N Numbers k such that k^4 + k + 1 is prime.
%C For s = 5,8,11,14,17,20,..., n_s = 1 + n + n^s is always composite for any n > 1. Also for n=1, n_s=3 is a prime for any s. Here we consider the case s=4.
%H T. D. Noe, <a href="/A049408/b049408.txt">Table of n, a(n) for n = 1..1000</a>
%e 26 is a term because at s=4, n=26, n_s = 1 + n + n^s = 457003 is a prime.
%t Select[Range[1000], PrimeQ[1 + # + #^4] &] (* _Vincenzo Librandi_, Jul 28 2014 *)
%o (PARI) for(n=1, 1000, if(isprime(1+n+n^4), print1(n",")))
%o (Magma) [n: n in [0..1000] | IsPrime(s) where s is 1+n+n^4]; // _Vincenzo Librandi_, Jul 28 2014
%Y Cf. A002384, A075723, A049407.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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