A136432 a(n)! is the smallest factorial bigger than n^n.

2, 2, 3, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87

Offset: 0

Author

Ben Paul Thurston, Apr 01 2008

Keywords

• easy
• nonn

Examples

			a(13) = 17 because 17! is the smallest factorial bigger than 13^13.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Programs

Mathematica

s = {2}; For[n = 1, n <= 1000, n++, For[k = Max[s], True, k++, If[k! > n^n, s = Union[s, {k}]; Break[]]]]; s (* Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008 *)
With[{ff=Table[{n,n!},{n,100}]},Transpose[Flatten[Table[Select[ff,#[[2]]>k^k&, 1],{k,90}],1]][[1]]] (* Harvey P. Dale, Mar 16 2013 *)

Formula

a(n) = A090529(n^n+1). - R. J. Mathar, Apr 06 2022

Extensions

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008

a(0) prepended by Alois P. Heinz, Mar 30 2022