A075715 Numbers n such that n^16 + n + 1 is prime.

1, 2, 21, 26, 47, 65, 99, 102, 206, 215, 216, 257, 294, 342, 437, 441, 537, 540, 702, 747, 837, 860, 909, 912, 921, 926, 942, 1020, 1071, 1101, 1112, 1125, 1181, 1254, 1266, 1322, 1344, 1364, 1370, 1406, 1422, 1665, 1814, 1821, 1829, 1905, 2024

Offset: 1

Author

Zak Seidov, Oct 03 2002

Keywords

• nonn
• easy

Comments

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).

Examples

			2 is in the sequence because 1 + 2 + 2^16 = 65539 is prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002384, A075714, A075716.

Programs

Magma

[n: n in [1..3000]| IsPrime(n^16+n+1)]; // Vincenzo Librandi, Dec 17 2013

Maple

A075715:=n->if type(1+n+n^16, prime) then n; fi; seq(A075715(n), n=1..3000); # Wesley Ivan Hurt, Dec 17 2013

Mathematica

Select[Range[3000], PrimeQ[#^16 + # + 1] &] (* Vincenzo Librandi, Dec 17 2013 *)

PARI

for(n=1,3000,if(isprime(1+n+n^16),print1(n",")))

Extensions

More terms from Ralf Stephan, Mar 19 2003