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%I #21 Sep 08 2022 08:45:07
%S 1,2,21,26,47,65,99,102,206,215,216,257,294,342,437,441,537,540,702,
%T 747,837,860,909,912,921,926,942,1020,1071,1101,1112,1125,1181,1254,
%U 1266,1322,1344,1364,1370,1406,1422,1665,1814,1821,1829,1905,2024
%N Numbers n such that n^16 + n + 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 at n = 1, n_s = 3 is a prime for any s. So it is interesting to consider only the cases of s =/= 5, 8, 11, 14, 17, 20, ... and n > 1. Here we consider the case s = 16 and find several first n's making n_s a prime (or a probable prime).
%H Vincenzo Librandi, <a href="/A075715/b075715.txt">Table of n, a(n) for n = 1..1000</a>
%e 2 is in the sequence because 1 + 2 + 2^16 = 65539 is prime.
%p A075715:=n->if type(1+n+n^16, prime) then n; fi; seq(A075715(n), n=1..3000); # _Wesley Ivan Hurt_, Dec 17 2013
%t Select[Range[3000], PrimeQ[#^16 + # + 1] &] (* _Vincenzo Librandi_, Dec 17 2013 *)
%o (PARI) for(n=1,3000,if(isprime(1+n+n^16),print1(n",")))
%o (Magma) [n: n in [1..3000]| IsPrime(n^16+n+1)]; // _Vincenzo Librandi_, Dec 17 2013
%Y Cf. A002384, A075714, A075716.
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Oct 03 2002
%E More terms from _Ralf Stephan_, Mar 19 2003
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