A075714 1+n+n^s is a prime, s=18.

1, 2, 9, 24, 27, 44, 80, 251, 263, 311, 332, 356, 366, 371, 458, 515, 546, 548, 561, 566, 597, 599, 608, 650, 674, 713, 717, 722, 746, 762, 855, 867, 909, 969, 989, 993, 1010, 1011, 1022, 1052, 1064, 1191, 1245, 1269, 1275, 1284, 1355, 1376, 1431, 1473

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=18 and find several first n's making n_s a prime (or a probable prime).

Examples

			2 is OK because at s=18, n=2, n_s=1+n+n^s=262147 is a prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A002384, A075713, A075715.

Programs

Magma

[n: n in [0..1600] | IsPrime(s) where s is 1+n+n^18]; // Vincenzo Librandi, Jul 28 2014

Mathematica

Select[Range[1800], PrimeQ[1 + # + #^18] &]  (* Harvey P. Dale, Mar 24 2011 *)

PARI

for(n=1,1000,if(isprime(1+n+n^18),print1(n",")))

Extensions

More terms from Ralf Stephan, Apr 05 2003