This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109616 #26 Aug 13 2025 19:28:01
%S A109616 2,5,10,25,36,44,65,67,138,149,176,212,279,1293,2367,2463,2707,3130,
%T A109616 4150,4635,6070,6355,10111,10560
%N A109616 Numbers k > 0 such that (10's complement factorial of k) + 1 is prime.
%C A109616 Larger values not certified.
%C A109616 Some of the larger entries may only correspond to probable primes.
%C A109616 a(25) > 16000. - _Michael S. Branicky_, Apr 27 2025
%e A109616 5 is a term because (10-5)*(10-4)*(10-3)*(10-2)*(10-1) + 1 = 15121 is prime.
%e A109616 10 is a term because (100-10)*(10-9)*..*(10-1) + 1 = 32659201 is prime.
%p A109616 b:= proc(n) option remember; `if`(n=0, 1,
%p A109616 (10^length(n)-n)*b(n-1))
%p A109616 end:
%p A109616 q:= n-> isprime(1+b(n)):
%p A109616 select(q, [$1..300])[]; # _Alois P. Heinz_, Aug 13 2025
%t A109616 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 *)
%Y A109616 Cf. A110396, A109617.
%K A109616 nonn,base,hard,more
%O A109616 1,1
%A A109616 _Jason Earls_, Aug 01 2005
%E A109616 a(14)-a(20) from _Ryan Propper_, May 20 2006
%E A109616 a(21)-a(24) from _Michael S. Branicky_, Apr 25 2025