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A134451
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Ternary digital root of n.
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8
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| Continued fraction expansion of sqrt(3) - 1. - N. J. A. Sloane (njas(AT)research.att.com), 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.
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 0..20000
Eric Weisstein's World of Mathematics, Ternary
Eric Weisstein's World of Mathematics, Digital Root
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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)], with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 29 2007
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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 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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PROG
| (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]
(Haskell)
a134451 = until (< 3) a053735
-- Reinhard Zumkeller, May 12 2011
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CROSSREFS
| Cf. A134452, A160390 (decimal expansion).
Sequence in context: A168361 A000034 A040001 * A167965 A167966 A167967
Adjacent sequences: A134448 A134449 A134450 * A134452 A134453 A134454
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KEYWORD
| nonn,base,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2007
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