login
Numbers k such that k! * F(k) + 1 is prime.
0

%I #10 Jun 30 2024 13:09:21

%S 1,2,3,4,5,7,8,10,11,15,41,98,149,193,233,265,403,898,935,1291,2079

%N Numbers k such that k! * F(k) + 1 is prime.

%C All values through 2079 have been proved prime with WinPFGW. No more terms up to 6700. Primality testing 2079!*F(2079)+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2087 Running N-1 test using base 2099 Calling Brillhart-Lehmer-Selfridge with factored part 33.88% 2079!*F(2079)+1 is prime! (15.2535s+0.0043s)

%C No more terms < 6729. - _David Wasserman_, Apr 24 2008

%C No more terms < 12000. - _Michael S. Branicky_, Jun 30 2024

%e a(6)=7 because 7!*fibonacci(7)+1 = 65521, a prime.

%t Select[Range[410],PrimeQ[#!Fibonacci[#]+1]&] (* The program generates the first 17 terms of the sequence. *) (* _Harvey P. Dale_, Jan 30 2024 *)

%Y Cf. A005443.

%K nonn,less

%O 1,2

%A _Jason Earls_, Mar 28 2005