A195535 - OEIS

A195535

Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(6).

5, 1020, 2247, 2633277900, 2640162496, 638843546289, 1396487515808, 6103353023795, 21860678072520, 82495605773137, 29466852345019792, 34041728665663572, 292320946605948260, 262936589866701605, 3964118460886936896

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OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..15.

MATHEMATICA

r = Sqrt[6]; 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}]] (* A195535, A195536 *)

Sqrt[a^2 + b^2] (* A195537 *)

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

CROSSREFS

Cf. A195500, A195536, A195537.

Sequence in context: A024072 A119549 A247593 * A004805 A220790 A372705

Adjacent sequences: A195532 A195533 A195534 * A195536 A195537 A195538

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved