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

1, 2, 4, 10, 26

Offset

1,2

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

Links

Table of n, a(n) for n=1..5.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A100604, A100858.

Sequence in context: A111564 A350507 A007021 * A247395 A183947 A154322

Adjacent sequences: A100602 A100603 A100604 * A100606 A100607 A100608

Keyword

nonn,hard,more

Author

Jonathan Vos Post, Nov 30 2004

Status

approved