A075713 1+n+n^19 is a prime.

1, 8, 15, 20, 29, 33, 48, 98, 105, 114, 177, 231, 260, 302, 320, 338, 387, 393, 432, 456, 473, 488, 489, 558, 564, 632, 677, 680, 726, 770, 795, 828, 855, 869, 1019, 1026, 1050, 1056, 1079, 1119, 1124, 1217, 1266, 1302, 1373, 1454, 1467, 1547

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=19 and find several first n's making n_s a prime (or a probable prime).

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1700

Crossrefs

Cf. A002384, A075714.

Programs

Magma

[n: n in [0..1600] | IsPrime(s) where s is 1+n+n^19]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[2000], PrimeQ[1 + # + #^19] &] (* Vincenzo Librandi, Jul 28 2014 *)

PARI

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

Extensions

More terms from Ralf Stephan, Mar 31 2003