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A189962
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Decimal expansion of 3*(1 + 3*sqrt(5))/11.
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3
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2, 1, 0, 2, 2, 3, 7, 4, 3, 6, 1, 3, 6, 1, 9, 1, 5, 6, 9, 7, 8, 9, 3, 2, 3, 9, 1, 0, 7, 8, 0, 1, 3, 5, 1, 0, 1, 7, 2, 4, 1, 4, 2, 2, 9, 4, 2, 2, 7, 6, 1, 1, 9, 5, 6, 2, 2, 1, 6, 4, 3, 2, 0, 0, 7, 9, 0, 4, 2, 6, 2, 1, 1, 8, 8, 5, 4, 7, 6, 7, 3, 5, 8, 8, 4, 5, 2, 0, 8, 7, 9, 5, 8, 2, 6, 4, 0, 0, 4, 3, 1, 5, 6, 8, 7, 0, 3, 2, 5, 9, 4, 1, 5, 4, 2, 1, 8, 6, 5, 0, 3, 4, 7, 9, 9, 4, 6, 3, 2, 0
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OFFSET
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1,1
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COMMENTS
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The constant at A189961 is the shape of a rectangle whose continued fraction partition consists of 4 golden rectangles. For a general discussion, see A188635.
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LINKS
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FORMULA
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Continued fraction (as explained at A188635): [r,r,r,r], where r = (1 + sqrt(5))/2. Ordinary continued fraction, as given by Mathematica program shown below:
[2,9,1,3,1,1,3,9,1,3,1,1,3,9,1,3,1,1,3,...]
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EXAMPLE
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2.10223743613619156978932391078013510172414229422761...
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MATHEMATICA
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r=(1+5^(1/2))/2;
FromContinuedFraction[{r, r, r, r}]
FullSimplify[%]
N[%, 130]
ContinuedFraction[%%]
RealDigits[3 (1+3*Sqrt[5])/11, 10, 150][[1]] (* Harvey P. Dale, Sep 11 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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