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A195577 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/5. 8
1, 4, 56, 299, 1020, 3180, 3901, 20944, 272996, 1465799, 4993800, 15577800, 19105801, 102585004, 1337133056, 7179484499, 24459629220, 76300063380, 93580208101, 502461329944, 6549277433996, 35165113611599, 119803258923600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..23.

MATHEMATICA

r = 3/5; z = 26;

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}]]  (* A195577, A195578 *)

Sqrt[a^2 + b^2] (* A195579 *)

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

CROSSREFS

Cf. A195500, A195578, A195579.

Sequence in context: A144138 A006592 A201448 * A255011 A201620 A204108

Adjacent sequences:  A195574 A195575 A195576 * A195578 A195579 A195580

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Sep 21 2011

EXTENSIONS

Typos in crossrefs fixed by Colin Barker, Jun 04 2015

STATUS

approved

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Last modified August 20 20:36 EDT 2018. Contains 313927 sequences. (Running on oeis4.)