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A190178
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Continued fraction of (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2.
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4
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3, 5, 1, 2, 1, 1, 1, 2, 1, 12, 1, 5, 1, 1, 2, 1, 14, 2, 9, 11, 1, 12, 1, 2, 1, 832, 1, 2, 2, 5, 1, 1, 17, 1, 2, 1, 9, 1, 12, 1, 1, 1, 6, 3, 2, 1, 1, 6, 3, 1, 1, 1, 2, 2, 1, 3, 1, 3, 3, 1, 2, 1, 45, 1, 1, 1, 1, 62, 9, 1, 1, 2, 3, 1, 6, 1, 3, 5, 1, 4
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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,r,1,...] where r=1+sqrt(2), the silver ratio. For geometric interpretations of both continued fractions, see A189977 and A188635.
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LINKS
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MATHEMATICA
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r = 1 + 2^(1/2));
FromContinuedFraction[{r, 1, {r, 1}}]
FullSimplify[%]
ContinuedFraction[%, 100] (* A190178 *)
RealDigits[N[%%, 120]] (* A190177 *)
N[%%%, 40]
ContinuedFraction[(1 + Sqrt[2] + Sqrt[7 + 6*Sqrt[2]])/2, 100] (* G. C. Greubel, Dec 28 2017 *)
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PROG
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(PARI) contfrac((1+sqrt(2)+sqrt(7+6*sqrt(2)))/2) \\ G. C. Greubel, Dec 28 2017
(Magma) ContinuedFraction((1+Sqrt(2)+Sqrt(7+6*Sqrt(2)))/2); // 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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