A064769 - OEIS

%I #26 Jan 12 2026 17:03:03

%S 1,2,3,5,9,17,65,222,1720,2975,3494,10489,17948

%N Numbers k such that (k!)^2 + prime(k) is prime.

%C Term <= 1720 certified prime with Primo.

%C Next term, if it exists, is greater than 2700. - _Ryan Propper_, Nov 05 2005

%C a(10)-a(13) are probable primes.

%C a(14) > 20000. - _Robert Price_, Aug 29 2014

%e (5!)^2 + prime(5) = 120^2 + 11 = 14400 + 11 = 14411 is prime, so 5 is a term.

%o (PARI) for(n=1,300, if(isprime((n!)^2+prime(n)),print1(n, ", ")))

%Y Cf. A046029, A072599 (n such that (n!)^2 - prime(n) is prime).

%K nonn,hard,more

%O 1,2

%A _Jason Earls_, Oct 18 2001

%E 1720 from _Ryan Propper_, Nov 05 2005

%E a(10)-a(13) from _Robert Price_, Aug 29 2014