OFFSET
1,1
COMMENTS
k = {3, 4, 29, 32, 133} yields primes p(n) = {5, 7, 109, 131, 751}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
a(6) > 600. - Jinyuan Wang, Apr 10 2020
a(6) > 2500. - Michael S. Branicky, Jul 02 2024
FORMULA
Numbers k such that (prime(k)-1)! + prime(k)^6 is prime, where prime(k) is the k-th prime.
EXAMPLE
a(1) = 3 because (prime(3)-1)! + prime(3)^6 = (5-1)! + 5^6 = 15649 is the smallest prime of that form.
MATHEMATICA
lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+p^6], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jonathan Vos Post, Nov 30 2004
EXTENSIONS
a(5) from Jinyuan Wang, Apr 10 2020
STATUS
approved