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A195532 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(5). 4
8, 5, 84, 2400, 1691, 11480, 118455, 352692, 1401961, 1663145124, 1802526192, 15798984680, 297278169720, 1479041362764, 1551248530483, 42254295673488, 1445285680561323, 28154300465964144, 49087267967218280, 373205366478956820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..20.

MATHEMATICA

r = Sqrt[5]; 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}]]  (* A195532, A195533 *)

Sqrt[a^2 + b^2] (* A195534 *)

(* by Peter J. C. Moses, Sep 02 2011 *)

CROSSREFS

Cf. A195500, A195533, A195534.

Sequence in context: A038283 A317402 A317574 * A106287 A239862 A276688

Adjacent sequences:  A195529 A195530 A195531 * A195533 A195534 A195535

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved

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Last modified February 25 06:46 EST 2020. Contains 332220 sequences. (Running on oeis4.)