A109616 Numbers k > 0 such that (10's complement factorial of k) + 1 is prime.

2, 5, 10, 25, 36, 44, 65, 67, 138, 149, 176, 212, 279, 1293, 2367, 2463, 2707, 3130, 4150, 4635, 6070, 6355, 10111, 10560

Offset: 1

Author

Jason Earls, Aug 01 2005

Keywords

• nonn
• base
• hard
• more

Comments

Larger values not certified.

Some of the larger entries may only correspond to probable primes.

a(25) > 16000. - Michael S. Branicky, Apr 27 2025

Examples

			5 is a term because (10-5)*(10-4)*(10-3)*(10-2)*(10-1) + 1 = 15121 is prime.
10 is a term because (100-10)*(10-9)*..*(10-1) + 1 = 32659201 is prime.
		

Crossrefs

Cf. A110396, A109617.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      (10^length(n)-n)*b(n-1))
    end:
q:= n-> isprime(1+b(n)):
select(q, [$1..300])[];  # Alois P. Heinz, Aug 13 2025

Mathematica

f[n_] := 10^Length[IntegerDigits[n]] - n; p = 1; Do[p *= f[n]; If[PrimeQ[p + 1], Print[n]], {n, 4635}] (* Ryan Propper, May 20 2006 *)

Extensions

a(14)-a(20) from Ryan Propper, May 20 2006

a(21)-a(24) from Michael S. Branicky, Apr 25 2025