%I A007623 M4678
%S A007623 0,1,10,11,20,21,100,101,110,111,120,121,200,201,210,211,220,221,300,301,
%T A007623 310,311,320,321,1000,1001,1010,1011,1020,1021,1100,1101,1110,1111,1120,
               1121,
%U A007623 1200,1201,1210,1211,1220,1221,1300,1301,1310,1311,1320,1321,2000,2001,
               2010
%N A007623 Integers written in factorial base.
%C A007623 Places reading from right have values (1, 2, 6, 24, 120, ...) = factorials.
%C A007623 Also the reversed inversion vectors for the list of all finite permutations 
               in reversed lexicographic order: A055089.
%C A007623 For large n it would be better to separate the "digits" by commas. - 
               M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Mar 27 2007
%D A007623 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007623 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, 
               MA, Vol. 2, p. 192.
%D A007623 F. Smarandache, Definitions solved and unsolved problems, conjectures 
               and theorems in number theory and geometry, edited by M. Perez, Xiquan 
               Publishing House, 2000.
%H A007623 M. F. Hasler, <a href="b007623.txt">Table of n, a(n) for n = 0..1000</
               a>
%H A007623 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Definitions-book.pdf">
               Definitions, Solved and Unsolved Problems, Conjectures, ... </a>
%H A007623 Wikipedia, <a href="http://en.wikipedia.org/wiki/Factoradic">Factorial 
               base</a>
%e A007623 a(47) = 1321 because 47 = 1*4! + 3*3! + 2*2! + 1*1!
%p A007623 a := n -> if nargs<2 then a(n,2) elif n<args[2] then n else a(iquo(n,
               args[2]),args[2]+1)*10+irem(n,args[2]) fi: 'a(i)'$i=0..200;
%t A007623 factBaseIntDs[n_] := Module[{m, i, len, dList, currDigit}, i = 1; While[n 
               > i!, i++ ]; m = n; len = i; dList = Table[0, {len}]; Do[ currDigit 
               = 0; While[m >= j!, m = m - j!; currDigit++ ]; dList[[len - j + 1]] 
               = currDigit, {j, i, 1, -1}]; If[dList[[1]] == 0, dList = Drop[dList, 
               1]]; dList]; Table[FromDigits[factBaseIntDs[n]], {n, 0, 50}] - Alonso 
               Delarte (alonso.delarte(AT)gmail.com), May 03 2006
%o A007623 (PARI): a(n,p=2) = if( n<p, n, a( n\p, p+1 )*10 + n%p ); vector(200,i,
               a(i-1)) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Mar 27 2007
%Y A007623 Cf. A000142. See also primorial base A049345, sum of digits A034968, 
               number of nonzero digits A060130. Simple algorithm fac_base given 
               in A055089.
%Y A007623 Cf. A060112, A060495. Permutation of A064039.
%Y A007623 Sequence in context: A037307 A165265 A049345 this_sequence A109827 A109839 
               A087486
%Y A007623 Adjacent sequences: A007620 A007621 A007622 this_sequence A007624 A007625 
               A007626
%K A007623 base,nonn,nice,easy
%O A007623 0,3
%A A007623 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Mira Bernstein (mira(AT)math.berkeley.edu)
%E A007623 More terms from R. K. Guy (rkg(AT)cpsc.ucalgary.ca)