%I A008904
%S A008904 1,1,2,6,4,2,2,4,2,8,8,8,6,8,2,8,8,6,8,2,4,4,8,4,6,4,4,8,4,6,8,8,6,
%T A008904 8,2,2,2,4,2,8,2,2,4,2,8,6,6,2,6,4,2,2,4,2,8,4,4,8,4,6,6,6,2,6,4,6,
%U A008904 6,2,6,4,8,8,6,8,2,4,4,8,4,6,8,8,6,8,2,2,2,4,2,8,2,2,4,2,8,6,6,2,6
%N A008904 Final nonzero digit of n!.
%C A008904 Jean-Paul Allouche (Jean-Paul.Allouche(AT)lri.fr), Jul 25, 2001: this 
               sequence is not ultimately periodic. This can be deduced from the 
               fact that the sequence can be obtained as a fixed point of a morphism.
%C A008904 The decimal number .1126422428... formed from these digits is a transcendental 
               number; see the article by G. Dresden. The Mathematica code uses 
               Dresden's formula for the last nonzero digit of n!; this is more 
               efficient than simply calculating n! and then taking its least-significant 
               digit. - Greg Dresden (dresdeng(AT)wlu.edu), Feb 21 2006
%D A008904 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 
               2003, p. 202.
%D A008904 F. M. Dekking, Regularity and irregularity of sequences generated by 
               automata, S\'em. Th\'eor. Nombres, Bordeaux, Expos\'e 9, 1979-1980, 
               pages 9-01 to 9-10.
%D A008904 Gregory P. Dresden, Three transcendental numbers from the last non-zero 
               digits of n^n, F_n and n!, Mathematics Magazine, pp. 96-105, vol. 
               81, 2008.
%D A008904 S. Kakutani, Ergodic theory of shift transformations, in Proc. 5th Berkeley 
               Symp. Math. Stat. Prob., Univ. Calif. Press, vol. II, 1967, 405-414.
%D A008904 J. C. Martin, The structure of generalized Morse minimal sets on m symbols, 
               Trans. Amer. Math. Soc. 232 (1977), 343-355.
%H A008904 T. D. Noe, <a href="b008904.txt">Table of n, a(n) for n=0..1000</a>
%H A008904 K. S. Brown, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/
               SEQUENCES/series020">The least significant nonzero digit of n!</a>
%H A008904 G. Dresden, <a href="http://home.wlu.edu/~dresdeng">Home page</a>.
%H A008904 MathPages, <a href="http://www.mathpages.com/home/kmath489.htm">Least 
               Significant Non-Zero Digit of n!</a>
%H A008904 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Factorial.html">Link to a section of The World of Mathematics.</a>
%H A008904 <a href="Sindx_Fi.html#final">Index entries for sequences related to 
               final digits of numbers</a>
%H A008904 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%F A008904 The generating function for n>1 is as follows: for n = a_0 + 5 a_1 + 
               5^2 a_2 + ... +5^N a_N (the expansion of n in base-5), then the last 
               nonzero digit of n!, for n>1, is 6*\prod_{i=0}^N (a_i)! (2^(i a_i)) 
               mod 10 - Greg Dresden (dresdeng(AT)wlu.edu), Feb 21 2006
%F A008904 a(n) = f(n,1,0) with f(n,x,e) = if n<2 then A010879(x*A000079(e)) else 
               f(n-1,A010879(x*A132740(n),e+A007814(n)-A112765(n)). [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 16 2008]
%e A008904 6! = 720, so a(6) = 2.
%t A008904 Do[m = n!; While[Mod[m, 10] == 0, m = m/10]; Print[Mod[m, 10]], {n, 0, 
               100}]
%t A008904 f[n_] := Mod[6Times @@ (Rest[FoldList[{ 1 + #1[[1]], #2!2^(#1[[1]]#2)} 
               &, {0, 0}, Reverse[IntegerDigits[n, 5]]]]), 10][[2]] (* program contributed 
               by Jacob A. Siehler *) - Greg Dresden (dresdeng(AT)wlu.edu), Feb 
               21 2006
%Y A008904 Cf. A008905, A000142.
%Y A008904 Sequence in context: A059574 A004600 A021795 this_sequence A074382 A061350 
               A046276
%Y A008904 Adjacent sequences: A008901 A008902 A008903 this_sequence A008905 A008906 
               A008907
%K A008904 nonn,base,nice
%O A008904 0,3
%A A008904 Russ Cox (rsc(AT)swtch.com)
%E A008904 More terms from Greg Dresden (dresdeng(AT)wlu.edu), Feb 21 2006