A195580 - OEIS

A195580

Denominators a(n) of Pythagorean approximations b(n)/a(n) to 4/5.

4, 600, 2600, 15996, 2460800, 10652800, 65552004, 10084355800, 43655173800, 268632095996, 41325687609600, 178898891577600, 1100854263840004, 169352657739783000, 733127614029833000, 4511300504584239996, 694007150091943126400

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OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..17.

MATHEMATICA

r = 4/5; z = 18;

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}]] (* A195580, A195611 *)

Sqrt[a^2 + b^2] (* A195612 *)

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

CROSSREFS

Cf. A195500, A195611, A195612.

Sequence in context: A102204 A086143 A123657 * A069641 A215920 A210853

Adjacent sequences: A195577 A195578 A195579 * A195581 A195582 A195583

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 21 2011

STATUS

approved