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
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.
Programs
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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
Comments