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 A134451 Ternary digital root of n. 21
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Continued fraction expansion of sqrt(3) - 1. - N. J. A. Sloane, Dec 17 2007. Cf. A040001, A048878/A002530. a(A005408(n)) = 1; a(A005843(n)) = 2 for n>0; a(n) = if n=0 then 0 else A000034(n-1). Minimum number of terms required to express n as a sum of odd numbers. Shadow transform of even numbers A005843. - Michel Marcus, Jun 06 2013 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform. N. J. A. Sloane, Transforms. Eric Weisstein's World of Mathematics, Ternary. Eric Weisstein's World of Mathematics, Digital Root. FORMULA a(n) = if n<=2 then n else a(A053735(n)). a(n) = -1/2+[(-1)^n]/2+2*[(n+2) mod (n+1)]. - Paolo P. Lava, Oct 29 2007 a(n) = ((n+1) mod 2) + 2*sign(n) - 1. - Wesley Ivan Hurt, Dec 06 2013 Multiplicative with a(2^e) = 2, a(p^e) = 1 for odd prime p. - Andrew Howroyd, Aug 06 2018 EXAMPLE n=42: A007089(42) = '1120', A053735(42) = 1+1+2+0 = 4, A007089(4)='11', A053735(4)=1+1=2: therefore a(42) = 2. 0.732050807568877293527446341... = 0 + 1/(1 + 1/(2 + 1/(1 + 1/(2 + ...)))) [Harry J. Smith, May 31 2009] MAPLE A134451:=n->((n+1) mod 2)+2*signum(n)-1; seq(A134451(n), n=0..100); # Wesley Ivan Hurt, Dec 06 2013 MATHEMATICA Table[Mod[n + 1, 2] + 2 Sign[n] - 1, {n, 0, 100}] (* Wesley Ivan Hurt, Dec 06 2013 *) PROG (PARI) { allocatemem(932245000); default(realprecision, 12000); x=contfrac(sqrt(3)-1); for (n=0, 20000, write("b134451.txt", n, " ", x[n+1])); } [Harry J. Smith, May 31 2009] (Haskell) a134451 = until (< 3) a053735 -- Reinhard Zumkeller, May 12 2011 CROSSREFS Cf. A134452, A160390 (decimal expansion). Related base-3 sequences: A053735, A134451, A230641, A230642, A230643, A230853, A230854, A230855, A230856, A230639, A230640, A010063 (trajectory of 1) Sequence in context: A107393 A000034 A040001 * A229217 A167965 A270370 Adjacent sequences:  A134448 A134449 A134450 * A134452 A134453 A134454 KEYWORD nonn,base,easy,mult AUTHOR Reinhard Zumkeller, Oct 27 2007 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)