A103740 Numbers k such that k! * F(k) + 1 is prime.

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

Offset

1,2

Comments

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)

No more terms < 6729. - David Wasserman, Apr 24 2008

No more terms < 12000. - Michael S. Branicky, Jun 30 2024

Links

Table of n, a(n) for n=1..21.

Example

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

Mathematica

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

Crossrefs

Cf. A005443.

Sequence in context: A305414 A373289 A317296 * A317578 A306435 A034155

Adjacent sequences: A103737 A103738 A103739 * A103741 A103742 A103743

Keyword

nonn,less

Author

Jason Earls, Mar 28 2005

Status

approved