%I A010879
%S A010879 0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,
%T A010879 7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,
%U A010879 4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0
%N A010879 Final digit of n.
%C A010879 Also decimal expansion of 137174210/1111111111 = 0.1234567890123456789012345678901234... 
               - Jason Earls (zevi_35711(AT)yahoo.com), Mar 19 2001
%C A010879 In general the base k expansion of A062808(k)/A048861(k) (k>=2) will 
               produce the numbers 0,1,2,...,k-1 repeated with period k, equivalent 
               to the sequence n mod k. The k-digit number in base k 123...(k-1)0 
               (base k) expressed in decimal is A062808(k), whereas A048861(k) = 
               k^k-1. In particular, A062808(10)/A048861(10)=1234567890/9999999999=137174210/
               1111111111.
%C A010879 n^5 mod 10. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 
               04 2009]
%H A010879 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A010879 <a href="Sindx_Fi.html#final">Index entries for sequences related to 
               final digits of numbers</a>
%F A010879 a(n)=n mod 10
%F A010879 Periodic with period 10.
%F A010879 a(n)=n mod 10. Complex representation: a(n)=1/10*(1-r^n)*sum{1<=k<10, 
               k*product{1<=m<10,m<>k, (1-r^(n-m))}} where r=exp(pi/5*i) and i=sqrt(-1). 
               Trigonometric representation: a(n)=(256/5)^2*(sin(n*pi/10))^2*sum{1<=k<10, 
               k*product{1<=m<10,m<>k, (sin((n-m)*pi/10))^2}}. G.f.: g(x)=(sum{1<=k<10, 
               k*x^k})/(1-x^10). Also: g(x)=x(9x^10-10x^9+1)/((1-x^10)(1-x)^2). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
%F A010879 a(n)=n mod 2+2*(floor(n/2)mod 5)=A000035(n)+2*A010874(A004526(n)). Also: 
               a(n)=n mod 5+5*(floor(n/5)mod 2)=A010874(n)+5*A000035(A002266(n)). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 11 2007
%F A010879 a(n)=10*{x/10}; Where {x} means fractional part of x [From Barbarel Tres 
               Mil (barbarel3000(AT)yahoo.es), Jul 30 2009]
%t A010879 Table[10*FractionalPart[n/10], {n, 1, 300}] [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), 
               Jul 30 2009]
%o A010879 (Other) sage: [power_mod(n,5,10)for n in xrange(0, 81)] # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Nov 04 2009]
%Y A010879 Cf. A034948, A059988, A048861, A062808.
%Y A010879 Partial sums: A130488. Other related sequences A130481, A130482, A130483, 
               A130484, A130485, A130486, A130487.
%Y A010879 Sequence in context: A004430 A134778 A118943 this_sequence A062078 A031347 
               A087471
%Y A010879 Adjacent sequences: A010876 A010877 A010878 this_sequence A010880 A010881 
               A010882
%K A010879 nonn,base,new
%O A010879 0,3
%A A010879 N. J. A. Sloane (njas(AT)research.att.com).