A075713 - OEIS

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

%S 1,8,15,20,29,33,48,98,105,114,177,231,260,302,320,338,387,393,432,

%T 456,473,488,489,558,564,632,677,680,726,770,795,828,855,869,1019,

%U 1026,1050,1056,1079,1119,1124,1217,1266,1302,1373,1454,1467,1547

%N 1+n+n^19 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=19 and find several first n's making n_s a prime (or a probable prime).

%H Vincenzo Librandi, <a href="/A075713/b075713.txt">Table of n, a(n) for n = 1..1700</a>

%e 8 is OK because at s=19, n=8, n_s=1+n+n^s=144115188075855881 is a prime.

%t Select[Range[2000], PrimeQ[1 + # + #^19] &] (* _Vincenzo Librandi_, Jul 28 2014 *)

%o (PARI) for(n=1, 2000, if(isprime(1+n+n^19), print1(n",")))

%o (Magma) [n: n in [0..1600] | IsPrime(s) where s is 1+n+n^19]; // _Vincenzo Librandi_, Jul 28 2014

%Y Cf. A002384, A075714.

%K nonn,easy

%O 1,2

%A _Zak Seidov_, Oct 03 2002

%E More terms from _Ralf Stephan_, Mar 31 2003