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%I #16 Feb 08 2023 07:23:10
%S 2,2,3,7,13,61,31,2521,20161,15121,604801,39916801,3991681,3113510401,
%T 14529715201,54486432001,10461394944001,59281238016001,53353114214401,
%U 2,670442572801,8515157028618240001,9366672731480064001
%N a(n) = largest prime of the form n!/k! + 1.
%C Is 19 the largest n such that a(n) = 2? There are none for 19 < n <= 600. - _Robert Israel_, Jan 16 2017
%H Robert Israel, <a href="/A093437/b093437.txt">Table of n, a(n) for n = 0..466</a>
%e a(7) = 2521 because 7!/2! + 1 = 2521 is prime, whereas 7!/1! + 1 = 5041 = 71^2 is composite;
%e a(19) = 2 because the only prime of the form 19!/k! + 1 is 19!/19! + 1 = 2.
%p f:= proc(n) local k,x;
%p x:= n!;
%p for k from 2 do
%p if isprime(x+1) then return x+1 fi;
%p x:= x/k;
%p od
%p end proc:
%p map(f, [$0..40]); # _Robert Israel_, Jan 16 2017
%t a[n_] := Module[{k, x}, x = n!; For[k = 2, True, k++, If[PrimeQ[x+1], Return[x+1]]; x = x/k]];
%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 08 2023, after _Robert Israel_ *)
%Y Cf. A093621 (smallest k > 0 such that n!/k! + 1 is prime), A002981 (n! + 1 is prime), A088332 (primes of form n! + 1).
%K nonn
%O 0,1
%A _Amarnath Murthy_, Apr 01 2004
%E Corrected and extended by _Hugo Pfoertner_, Apr 06 2004
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