A137322 - OEIS

%I #16 Mar 12 2022 07:55:42

%S 2,93,1915,2805257,1022362697389,52812321503747,296760465891270915823,

%T 13532790387670672394876021,244372391812343146601953447089433,

%U 11196066938065133911754151366849886273516531,3328707950474207400029638710843582600755265569

%N a(n) = k! - A051674(n), where k is the smallest number for which A051674(n) <= k! where A051674(n) = prime(n)^prime(n).

%e a(4) = 10! - prime(4)^prime(4) = 3628800 - 823543 = 2805257.

%t a[n_] := Module[{p = Prime[n]^Prime[n], k = 1}, While[k! < p, k++]; k! - p]; Array[a, 11] (* _Amiram Eldar_, Mar 12 2022 *)

%o (PARI) f(n) = my(p = prime(n)); p^p;

%o a(n) = my(k=1, P=f(n)); until(k! >= P, k++); k!-P; \\ _Michel Marcus_, Mar 12 2022

%Y Cf. A000040, A000142, A051674, A136437.

%K easy,nonn

%O 1,1

%A _Ctibor O. Zizka_, Apr 06 2008

%E Corrected and extended by _Michel Marcus_, Mar 12 2022