Search: id:A010888
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%I A010888
%S A010888 0,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,
%T A010888 8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,
%U A010888 7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,1,2,3,4,5
%N A010888 Digital root of n (repeatedly add digits until reach a single digit).
%C A010888 Decimal expansion of 13717421/111111111 is 0.123456789123456789123456789... 
               with period 9. - Eric Desbiaux (moongerms(AT)wanadoo.fr), May 19 
               2008
%C A010888 Partial sums are given by A130487(n-1)+n (for n>0). - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Jun 08 2007
%H A010888 N. J. A. Sloane, <a href="b010888.txt">Table of n, a(n) for n = 0..10000</
               a>
%H A010888 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Digitaddition.html">Link to a section of The World of Mathematics.</
               a>
%H A010888 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitalRoot.html">Link to a section of The World of Mathematics.</
               a>
%F A010888 If n=0 then a(n) = 0; otherwise a(n) = (n reduced mod 9), but if the 
               answer is 0 change it to 9.
%F A010888 Equivalently, if n=0 then a(n) = 0, otherwise a(n) = (n-1 reduced mod 
               9) + 1.
%F A010888 Has period 9.
%F A010888 a(n)=A010878(n-1)+1 (for n>0). - G.f.: g(x)=(x*sum{0<=k<9, (k+1)*x^k})/
               (1-x^9). Also: g(x)=x(9x^10-10x^9+1)/((1-x^9)(1-x)^2). - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 08 2007
%F A010888 a(n) = 1+[(n+8) mod 9]-9*{1-[((n+1)!+1) mod (n+1)]}, with n>=0. a(n) 
               = 1+[(n+8) mod 9]-9*A000007 - Paolo P. Lava (ppl(AT)spl.at), Jun 
               20 2007
%e A010888 37 -> 10 -> 1, so a(37)=1.
%p A010888 P:=proc(n) local a,i; for i from 0 by 1 to n do a:=1+((i+8) mod 9)-9*(1-(((i+1)!+1) 
               mod (i+1))); print(a); od; end: P(100); - Paolo P. Lava (ppl(AT)spl.at), 
               Jun 20 2007
%t A010888 Join[{0}, Array[Mod[ # - 1, 9] + 1 &, 104]] (from Robert G. Wilson v 
               (rgwv(at)rgwv.com), Jan 04 2006)
%Y A010888 Cf. A007953, A007954, A031347, A113217, A113218.
%Y A010888 Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010879, A004526, 
               A002264, A002265, A002266.
%Y A010888 Sequence in context: A037265 A053837 A128244 this_sequence A131650 A033930 
               A076314
%Y A010888 Adjacent sequences: A010885 A010886 A010887 this_sequence A010889 A010890 
               A010891
%K A010888 nonn,easy,nice,base
%O A010888 0,3
%A A010888 N. J. A. Sloane (njas(AT)research.att.com).

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