A126017 Smallest prime of the form k^n + k^(n-1) - 1.

2, 5, 11, 23, 47, 971, 191, 383, 22136835839, 1310719, 2259801991, 6143, 353563778431304822783, 91424858111, 5425784582791, 57395627, 21474836479, 1099999999999999999, 786431, 13508517176729920889, 1818426107493966837974532393806148403199, 153558654482644991

Offset: 1

Author

Artur Jasinski, Dec 14 2006

Keywords

• nonn

Comments

Primes arising in A125973.

Examples

			Consider n = 10. k^n + k^(n-1) - 1 evaluates to 1, 1535, 78731, 1310719 for k = 1, ..., 4. Only the last of these numbers, 4^10+4^9-1 = 1310719, is prime, hence a(10) = 1310719.
		

Crossrefs

Cf. A000040, A045546, A125881-A125885, A125965-A125973.

Programs

Mathematica

Table[k=0;Until[PrimeQ[p=k^n+k^(n-1)-1],k++];p,{n,22}] (* James C. McMahon, Dec 23 2024 *)

PARI

{for(n=1,20,k=1;while(!isprime(a=k^n+k^(n-1)-1),k++);print1(a,","))} \\ Klaus Brockhaus, Dec 17 2006

Extensions

Edited and extended by Klaus Brockhaus, Dec 17 2006

a(21)-a(22) from James C. McMahon, Dec 23 2024