%I #16 Jul 02 2024 14:19:18
%S 1,2,4,10,26
%N Numbers k such that (prime(k)-1)! + prime(k)^2 is prime.
%C 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.
%C a(6) > 750. - _Jinyuan Wang_, Apr 10 2020
%C a(5) > 2500. - _Michael S. Branicky_, Jul 02 2024
%F Numbers k such that (prime(k)-1)! + prime(k)^2 is prime, where prime(k) is the k-th prime.
%e 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.
%o (PARI) is(k) = ispseudoprime((prime(k)-1)! + prime(k)^2); \\ _Jinyuan Wang_, Apr 10 2020
%Y Cf. A100604, A100858.
%K nonn,hard,more
%O 1,2
%A _Jonathan Vos Post_, Nov 30 2004