A075716 - OEIS

%I #14 Sep 08 2022 08:45:07

%S 1,2,30,32,35,54,62,77,101,120,138,161,171,186,210,234,269,285,311,

%T 341,362,368,374,467,476,486,531,567,578,720,737,740,780,806,824,932,

%U 990,1035,1037,1041,1049,1067,1089,1136,1137,1146,1167,1202,1251,1269

%N 1+n+n^s is a prime, s=15.

%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=15 and find several first n's making n_s a prime (or a probable prime).

%H Vincenzo Librandi, <a href="/A075716/b075716.txt">Table of n, a(n) for n = 1..2000</a>

%e 2 is OK because at s=15, n=2, n_s=1+n+n^s=32771 is a prime.

%t Select[Range[1500], PrimeQ[1 + # + #^15] &] (* _Harvey P. Dale_, Dec. 13, 2010 *)

%t Select[Range[2000], PrimeQ[Total[#^Range[1, 15, 14]] + 1] &] (* _Vincenzo Librandi_, Jul 28 2014 *)

%o (PARI) for(n=1,1000,if(isprime(1+n+n^15),print1(n",")))

%o (Magma) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^15]; // _Vincenzo Librandi_, Jul 28 2014

%Y Cf. A002384, A075715, A075717.

%K nonn,easy

%O 1,2

%A _Zak Seidov_, Oct 03 2002

%E More terms from _Ralf Stephan_, Apr 05 2003