A100605 Numbers k such that (prime(k)-1)! + prime(k)^2 is prime.

1, 2, 4, 10, 26

Offset: 1

Author

Jonathan Vos Post, Nov 30 2004

Keywords

• nonn
• hard
• more

Comments

k = {1, 2, 4, 10, 26} yields primes p(k) = {2, 3, 7, 29, 101}. There are no more such k up to k=100. Verified by Ray Chandler.

a(6) > 750. - Jinyuan Wang, Apr 10 2020

a(5) > 2500. - Michael S. Branicky, Jul 02 2024

Examples

			a(3) = 4 because (prime(4)-1)! + prime(4)^2 = (7-1)! + 7^2 = 720 + 49 = 769 is prime and is the 3rd such prime of that form.
		

Crossrefs

Cf. A100604, A100858.

Programs

PARI

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^2); \\ Jinyuan Wang, Apr 10 2020

Formula

Numbers k such that (prime(k)-1)! + prime(k)^2 is prime, where prime(k) is the k-th prime.