A075717 1+n+n^13 is a prime.

1, 5, 15, 39, 50, 56, 105, 116, 128, 153, 168, 170, 243, 245, 264, 308, 314, 369, 401, 429, 480, 489, 531, 551, 599, 608, 680, 690, 699, 701, 785, 804, 939, 978, 1050, 1056, 1065, 1073, 1110, 1169, 1224, 1226, 1271, 1283, 1308, 1310, 1391, 1401

Offset

1,2

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 I consider the case s=13 and find several first n's making n_s a prime (or a probable prime).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1900

Example

5 is OK because at s=13, n=2, n_s=1+n+n^s=1220703131 is a prime.

Mathematica

Select[Range[1500], PrimeQ[1 + # + #^13] &] (* Harvey P. Dale, Apr 20 2013 *)

Prog

(PARI) n=0; for(k=1, 60, n=n+1; while(!isprime(1+n+n^13), n=n+1); print1(n", "))
(Magma) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^13]; // Vincenzo Librandi, Jul 28 2014

Crossrefs

Cf. A002384, A075716, A075718.

Sequence in context: A050488 A188282 A014316 * A062487 A084447 A357290

Adjacent sequences: A075714 A075715 A075716 * A075718 A075719 A075720

Keyword

nonn,easy

Author

Zak Seidov, Oct 03 2002

Extensions

More terms from Ralf Stephan, Mar 20 2003

Status

approved