login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A116983 Position of n! among the lexicographically ordered permutations of digits of n!. 1
1, 1, 1, 1, 1, 4, 6, 11, 54, 150, 648, 5013, 9849, 19345, 1060707, 10939036, 4343045, 2498014850, 5271260976, 78029366100, 531495923280, 805809810981, 1936900666393, 28724010464057580, 29052364970866225, 75805259574286872, 7466893805506395652, 80374513001512054041 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
Robert Israel and Vladimir Letsko, Table of n, a(n) for n = 0..422 (a(0) to a(100) from Vladimir Letsko)
EXAMPLE
a(5)=4 because 5!=120 and {1,2,0} is the 4th of the 6 permutations of {0,1,2} when listed in lexicographical order: {{0,1,2},{0,2,1},{1,0,2},{1,2,0},{2,0,1},{2,1,0}}.
a(14)=1060707 because 14!=87178291200 and {8,7,1,7,8,2,9,1,2,0,0} is the 1060707th of the 1247400 permutations of {0,0,1,1,2,2,7,7,8,8,9} when listed in lexicographical order.
MAPLE
for y to 1000 do N:=y!:s:=floor(log10(N))+1:a:=array(1..10): for i to 10 do a[i]:=0:od: c:=array(1..s):for j to s do c[j]:=floor(N/10^(j-1))-10*floor(N/10^j):od: for i to s do k:=c[i]:a[k+1]:=a[k+1]+1:od: q:=1:p:=s!/(a[10]!*a[1]!*a[2]!*a[3]!*a[4]!*a[5]!*a[6]!*a[7]!*a[8]!*a[9]!): for j from s by -1 to 2 do p:=p/j; r:=c[j]; if r>0 then for t from 0 to r-1 do if a[t+1]>0 then q:=q+p*a[t+1]:fi:od:fi:p:=p*a[r+1]:a[r+1]:=a[r+1]-1:od:print(y, N, q):od: # Anatoly Kazmerchuk, Jun 06 2009
f:= proc(X)
local L, Lp, T, d, i, t;
if nops(X) = 1 then return 1 fi;
L:= [seq(numboccur(i, X), i=0..9)];
T:= 0;
for d from 0 to X[1]-1 do
if L[d+1] > 0 then
Lp:= L - [0$d, 1, 0$(9-d)];
T:= T + convert(Lp, `+`)!/mul(t!, t=Lp);
fi
od:
T + procname(X[2..-1]);
end proc:
seq(f(ListTools:-Reverse(convert(n!, base, 10))), n=1..50); # Robert Israel, Dec 22 2014
MATHEMATICA
Do[per=Permutations[Sort[tn=IntegerDigits[n! ]]]; Print[Position[per, tn]], {n, 0, 14}]
lst={}; Do[p=Permutations[Sort[i=IntegerDigits[n! ]]]; AppendTo[lst, FromDigits[FromDigits[Position[p, i]]]], {n, 0, 14}]; lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
CROSSREFS
Sequence in context: A358913 A066155 A105308 * A196271 A078426 A212558
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Apr 01 2006
EXTENSIONS
More terms from Vladimir Letsko, Jun 17 2009
Keyword "base" added by Max Alekseyev, Jul 03 2009
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)