A380903 Least positive k such that n^n * k^k - 1 is a prime, or 0 if no such k exists.

2, 2, 1, 2, 3, 4, 10147, 24

Offset: 0

Author

Jason Yuen, Feb 07 2025

Keywords

• nonn
• hard
• more

Comments

a(8) > 10^5 or a(8) = 0.

a(9) = 0, a(10) = 3, a(11) = 3142, a(12) = 559, a(13) = 3558.

a(14) > 10^5 or a(14) = 0.

Examples

			The least k > 0 such that 4^4*k^k - 1 is a prime is k = 3, so a(4) = 3.
		

Crossrefs

Cf. A228175, A231119, A231735.

Programs

PARI

a(n) = for(k=1, oo, if(ispseudoprime(n^n*k^k-1), return(k))) \\ Does not terminate if a(n) = 0.

Formula

a(n) = A231735(n^n).