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

0,3

Comments

!n is a subfactorial number (A000166).

Links

Table of n, a(n) for n=0..63.

Example

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.

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 *)

Crossrefs

Cf. A000166, A018799.

Sequence in context: A217013 A058991 A341860 * A090786 A127818 A320261

Adjacent sequences: A197420 A197421 A197422 * A197424 A197425 A197426

Keyword

nonn,base

Author

Michel Lagneau, Oct 14 2011

Extensions

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

Status

approved