A135996 Difference between 2^n and the largest factorial <= 2^n.

0, 0, 2, 2, 10, 8, 40, 8, 136, 392, 304, 1328, 3376, 3152, 11344, 27728, 25216, 90752, 221824, 161408, 685696, 1734272, 565504, 4759808, 13148416, 29925632, 27192064, 94300928, 228518656, 57869312, 594740224, 1668482048, 3815965696, 2362913792

Offset: 0

Author

Ctibor O. Zizka, Mar 03 2008, Mar 16 2008

Keywords

• easy
• nonn

Examples

			a(6) = 2^6 - 4! = 40
a(7) = 2^7 - 5! = 8
a(8) = 2^8 - 5! = 136
		

Crossrefs

Cf. A000142.

Programs

Maple

A048764 := proc(n) local a; for a from 1 do if a! > n then RETURN((a-1)!); fi ; od: end: A135996 := proc(n) 2^n-A048764(2^n) ; end: seq(A135996(n),n=0..60) ; # R. J. Mathar, Mar 16 2008

Mathematica

d2n[n_]:=Module[{n2=2^n,fcts=Reverse[Range[100]!]},n2-Select[fcts,#<= n2&,1]]; Flatten[Array[d2n,40,0]] (* Harvey P. Dale, Aug 22 2012 *)

Formula

a(n) = 2^n - A048764(2^n). - R. J. Mathar, Mar 16 2008

Extensions

More terms from R. J. Mathar, Mar 16 2008