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A190183
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Continued fraction of (1+x+sqrt(8+2x))/4, where x=sqrt(15).
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2
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2, 4, 1, 3, 10, 1, 3, 1, 1, 2, 66, 1, 4, 2, 1, 1, 48, 5, 1, 1, 2, 1, 1, 1, 8, 2, 1, 1, 4, 16, 2, 2, 1, 4, 1, 3, 1, 3, 1, 11, 1, 1, 8, 16, 1, 1, 1, 10, 1, 2, 4, 1, 1, 1, 3, 1, 1, 1, 1, 30, 1, 1, 2, 1, 1, 8, 13, 1, 1, 6, 6, 1, 6, 1, 1, 2, 2, 10, 1, 2, 7, 9, 2, 4, 7, 3, 1, 2, 2, 1, 2, 5, 4, 2, 3, 2, 3, 2, 1, 3
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OFFSET
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1,1
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COMMENTS
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Equivalent to the periodic continued fraction [r,1,1,r,1,1,...] where r=(1+sqrt(5))/2, the golden ratio. For geometric interpretations of both continued fractions, see A190182 and A188635.
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LINKS
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MATHEMATICA
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r = (1 + 5^(1/2))/2;
FromContinuedFraction[{r, 1, 1, {r, 1, 1}}]
FullSimplify[%]
ContinuedFraction[%, 100] (* A190183 *)
RealDigits[N[%%, 120]] (* A190182 *)
N[%%%, 40]
ContinuedFraction[(1+Sqrt[15]+Sqrt[8+2Sqrt[15]])/4, 100] (* Harvey P. Dale, Apr 29 2013 *)
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PROG
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(PARI) contfrac((1+sqrt(15)+sqrt(8+2*sqrt(15)))/4) \\ G. C. Greubel, Dec 28 2017
(Magma) ContinuedFraction((1+Sqrt(15)+Sqrt(8+2*Sqrt(15)))/4); // G. C. Greubel, Dec 28 2017
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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STATUS
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approved
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