A075716 1+n+n^s is a prime, s=15.

1, 2, 30, 32, 35, 54, 62, 77, 101, 120, 138, 161, 171, 186, 210, 234, 269, 285, 311, 341, 362, 368, 374, 467, 476, 486, 531, 567, 578, 720, 737, 740, 780, 806, 824, 932, 990, 1035, 1037, 1041, 1049, 1067, 1089, 1136, 1137, 1146, 1167, 1202, 1251, 1269

Offset: 1

Author

Zak Seidov, Oct 03 2002

Keywords

• nonn
• easy

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

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A002384, A075715, A075717.

Programs

Magma

[n: n in [0..2000] | IsPrime(s) where s is 1+n+n^15]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[1500], PrimeQ[1 + # + #^15] &] (* Harvey P. Dale, Dec 13 2010 *)
Select[Range[2000], PrimeQ[Total[#^Range[1, 15, 14]] + 1] &] (* Vincenzo Librandi, Jul 28 2014 *)

PARI

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

Extensions

More terms from Ralf Stephan, Apr 05 2003