A075718 - OEIS

%I #12 Sep 08 2022 08:45:07

%S 1,2,14,30,32,44,65,87,90,122,134,149,162,186,189,227,237,249,255,266,

%T 311,354,366,456,476,485,561,567,584,597,605,650,665,672,689,720,771,

%U 819,884,899,975,990,1059,1082,1092,1191,1200,1241,1257,1295,1347,1367

%N 1+n+n^s is a prime, s=12.

%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 i consider the case s=12 and find several first n's making n_s a prime (or a probable prime).

%H Vincenzo Librandi, <a href="/A075718/b075718.txt">Table of n, a(n) for n = 1..2200</a>

%e 2 is OK because at s=12, n=2, n_s=1+n+n^s=4099 is a prime.

%t Select[Range[2000], PrimeQ[1 + # + #^12] &] (* _Vincenzo Librandi_, Jul 28 2014 *)

%o (PARI) for(n=1,1000,if(isprime(1+n+n^12),print1(n",")))

%o (Magma) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^12]; // _Vincenzo Librandi_, Jul 28 2014

%Y Cf. A002384, A075717, A075719.

%K nonn,easy

%O 1,2

%A _Zak Seidov_, Oct 03 2002

%E More terms from _Ralf Stephan_, Apr 05 2003