A353122 Numbers k such that k^k*(k+1) + 1 is prime.

0, 1, 2, 3, 6, 9, 186, 198, 8390

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 24 2022

Keywords

• nonn
• hard
• more

Comments

Corresponding primes start 2, 3, 13, 109, 326593, 3874204891, ...

a(9) > 6000. - Jon E. Schoenfield, Jun 05 2022

a(10) > 18000. - Michael S. Branicky, Aug 08 2024

Examples

			9 is in the sequence because 9^9*(9+1) + 1 = 3874204891, which is prime.
		

Crossrefs

Cf. A055897, A081132, A108318, A108879, A191513, A191568, A271718.

Programs

Magma

[n: n in [0..200] | IsPrime(n^n*(n+1) + 1)];

Mathematica

Join[{0}, Select[Range[200], PrimeQ[#^#*(# + 1) + 1] &]] (* Amiram Eldar, Apr 25 2022 *)

PARI

isok(k) = ispseudoprime(k^k*(k+1) + 1); \\ Michel Marcus, May 16 2022

Extensions

a(9) from Michael S. Branicky, Dec 22 2023