A195687 - OEIS

A195687

Denominators a(n) of Pythagorean approximations b(n)/a(n) to (1+sqrt(5))/2 (the golden ratio).

3, 8, 28, 1863, 4400, 433008, 262353, 352207108, 379920428, 18418959496, 91011249895, 978117768540, 11516765628956, 1219780690817560, 708294344602810604, 25852535312829023356, 229222230912132985022679

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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 = GoldenRatio; 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}]] (* A195687, A195688 *)

Sqrt[a^2 + b^2] (* A195689 *)

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

CROSSREFS

Cf. A195500, A195681, A195682.

Sequence in context: A268302 A345177 A342139 * A060707 A080874 A148867

Adjacent sequences: A195684 A195685 A195686 * A195688 A195689 A195690

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 22 2011

STATUS

approved