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 A195687 Denominators a(n) of Pythagorean approximations b(n)/a(n) to (1+sqrt(5))/2 (the golden ratio). 4
 3, 8, 28, 1863, 4400, 433008, 262353, 352207108, 379920428, 18418959496, 91011249895, 978117768540, 11516765628956, 1219780690817560, 708294344602810604, 25852535312829023356, 229222230912132985022679 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A195500 for a discussion and references. LINKS MATHEMATICA r = GoldenRatio; z = 24; p[{f_, n_}] := (#1[[2]]/#1[[       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[      Array[FromContinuedFraction[         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]]; {a, b} = ({Denominator[#1], Numerator[#1]} &)[p[{r, z}]]  (* A195687, A195688 *) Sqrt[a^2 + b^2] (* A195689 *) (* Peter J. C. Moses, Sep 02 2011 *) CROSSREFS Cf. A195500, A195681, A195682. Sequence in context: A327030 A000239 A268302 * A060707 A080874 A148867 Adjacent sequences:  A195684 A195685 A195686 * A195688 A195689 A195690 KEYWORD nonn AUTHOR Clark Kimberling, Sep 22 2011 STATUS approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)