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A195538 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(8). 4
5, 12, 145, 420, 4901, 14280, 166465, 485112, 5654885, 16479540, 192099601, 559819260, 6525731525, 19017375312, 221682772225, 646030941360, 7530688524101, 21946034630940, 255821727047185, 745519146510612, 8690408031080165 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

Conjecture: a(n) = 35*a(n-2) - 35*a(n-4) + a(n-6) with bisections A098602 and A076218. - R. J. Mathar, Sep 21 2011

LINKS

Table of n, a(n) for n=1..21.

MATHEMATICA

r = Sqrt[8]; 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}]]  (* A195538, A195539 *)

Sqrt[a^2 + b^2] (* A195540 *)

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

CROSSREFS

Cf. A195500, A195539, A195540.

Sequence in context: A009754 A096314 A323565 * A047658 A290804 A146542

Adjacent sequences:  A195535 A195536 A195537 * A195539 A195540 A195541

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved

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Last modified November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)