A197423 Smallest integer m such that !m begins with n in base 10.

1, 0, 3, 14, 5, 25, 69, 16, 20, 4, 34, 28, 41, 9, 8, 53, 73, 12, 7, 38, 46, 81, 13, 18, 120, 138, 6, 156, 186, 52, 31, 33, 14, 166, 98, 97, 96, 104, 35, 105, 27, 22, 93, 146, 5, 48, 55, 249, 15, 91, 37, 42, 187, 77, 90, 124, 352, 25, 110, 394, 89, 280, 69, 147

Offset: 0

Author

Michel Lagneau, Oct 14 2011

Keywords

• nonn
• base

Comments

!n is a subfactorial number (A000166).

Examples

			Subfactorial(0) = 1 begins with 1, so a(1) = 0 ;
Subfactorial(3) = 2 begins with 2, so a(2) = 3 ;
Subfactorial(14) = 32071101049 begins with 3, so a(3) = 14.
		

Crossrefs

Cf. A000166, A018799.

Programs

Maple

for n from 1 to 100 do:l1:=length(n):i:=0:for m from 1 to 400 while(i=0)do:
s:=0:for j from 0 to m do: s:=s+m!*(((-1)^j)*1/j!) :od:x:=s:l:=length(x):y:=floor(x/(10^(l-l1))):if y=n and l>=l1 then i:=1: printf ( "%d %d \n",n,m): else fi:od:od:

Mathematica

f[n_] := Block[{k = 0, m}, While[m = Max[0, Floor@Log[10, Subfactorial[k]] - Floor@Log[10, n]]; (Subfactorial[k] - Mod[Subfactorial[k], 10^m])/10^m! = n, k++]; k]; Array[f, 67] (* program from David W. Wilson - see A018799 Nov 05 2010 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 02 2017