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A195571 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 1/5. 4
1, 40, 60, 99, 4100, 6100, 10101, 418140, 622160, 1030199, 42646200, 63454200, 105070201, 4349494240, 6471706260, 10716130299, 443605766300, 660050584300, 1092940220301, 45243438668340, 67318687892360, 111469186340399, 4614387138404400 (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.

FORMULA

Conjecture: a(n) = 101*a(n-3) + 101*a(n-6) - a(n-9). - R. J. Mathar, Sep 21 2011

Empirical g.f.: x*(x^6+40*x^5+60*x^4-2*x^3+60*x^2+40*x+1) / (x^9-101*x^6-101*x^3+1). - Colin Barker, Jun 04 2015

MATHEMATICA

r = 1/5; 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}]]  (* A195571, A195572 *)

Sqrt[a^2 + b^2] (* A195573 *)

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

CROSSREFS

Cf. A195500, A195572, A195573.

Sequence in context: A094619 A052475 A182205 * A060672 A204754 A204747

Adjacent sequences:  A195568 A195569 A195570 * A195572 A195573 A195574

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 21 2011

STATUS

approved

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Last modified May 25 20:58 EDT 2020. Contains 334597 sequences. (Running on oeis4.)