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A195565 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/4. 4
4, 3, 204, 280, 2280, 12596, 12797, 831996, 1149440, 9341440, 51622404, 52441603, 3409523404, 4710402840, 38281220840, 211548594996, 214905676797, 13972226073596, 19303229690880, 156876433658880, 866926090675204, 880683411072003 (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..22.

MATHEMATICA

r = 5/4; 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}]]  (* A195565, A195566 *)

Sqrt[a^2 + b^2] (* A195567 *)

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

CROSSREFS

Cf. A195500, A195566, A195567.

Sequence in context: A325871 A079324 A002298 * A335913 A197243 A175372

Adjacent sequences:  A195562 A195563 A195564 * A195566 A195567 A195568

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 21 2011

STATUS

approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)