A075717 - OEIS

%I #17 Sep 08 2022 08:45:07

%S 1,5,15,39,50,56,105,116,128,153,168,170,243,245,264,308,314,369,401,

%T 429,480,489,531,551,599,608,680,690,699,701,785,804,939,978,1050,

%U 1056,1065,1073,1110,1169,1224,1226,1271,1283,1308,1310,1391,1401

%N 1+n+n^13 is a 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 I consider the case s=13 and find several first n's making n_s a prime (or a probable prime).

%H Vincenzo Librandi, <a href="/A075717/b075717.txt">Table of n, a(n) for n = 1..1900</a>

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

%t Select[Range[1500], PrimeQ[1 + # + #^13] &] (* _Harvey P. Dale_, Apr 20 2013 *)

%o (PARI) n=0; for(k=1, 60, n=n+1; while(!isprime(1+n+n^13), n=n+1); print1(n","))

%o (Magma) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^13]; // _Vincenzo Librandi_, Jul 28 2014

%Y Cf. A002384, A075716, A075718.

%K nonn,easy

%O 1,2

%A _Zak Seidov_, Oct 03 2002

%E More terms from _Ralf Stephan_, Mar 20 2003