Search: id:A134451
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%I A134451
%S A134451 0,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
%T A134451 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,
%U A134451 2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2
%N A134451 Ternary digital root of n.
%C A134451 Continued fraction expansion of sqrt(3) - 1. - N. J. A. Sloane (njas(AT)research.att.com), 
               Dec 17 2007. Cf. A040001, A048878/A002530.
%C A134451 a(A005408(n)) = 1; a(A005843(n)) = 2 for n>0;
%C A134451 a(n) = if n=0 then 0 else A000034(n-1).
%H A134451 Harry J. Smith, <a href="b134451.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A134451 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Ternary.html">Ternary</a>
%H A134451 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitalRoot.html">Digital Root</a>
%F A134451 a(n) = if n<=2 then n else a(A053735(n)).
%F A134451 a(n) = -1/2+[(-1)^n]/2+2*[(n+2) mod (n+1)], with n>=0 - Paolo P. Lava 
               (ppl(AT)spl.at), Oct 29 2007
%e A134451 n=42: A007089(42) = '1120', A053735(42) = 1+1+2+0 = 4,
%e A134451 A007089(4)='11', A053735(4)=1+1=2: therefore a(42) = 2.
%e A134451 0.732050807568877293527446341... = 0 + 1/(1 + 1/(2 + 1/(1 + 1/(2 + ...)))) 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
%o A134451 (PARI) { allocatemem(932245000); default(realprecision, 12000); x=contfrac(sqrt(3)-1); 
               for (n=0, 20000, write("b134451.txt", n, " ", x[n+1])); } [From Harry 
               J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
%Y A134451 Cf. A134452.
%Y A134451 Cf. A160390 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 31 2009]
%Y A134451 Sequence in context: A063435 A000034 A040001 this_sequence A160990 A160989 
               A066788
%Y A134451 Adjacent sequences: A134448 A134449 A134450 this_sequence A134452 A134453 
               A134454
%K A134451 nonn
%O A134451 0,3
%A A134451 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2007

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