A195553 - OEIS

A195553

Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/2.

5, 260, 7020, 94635, 5103280, 137599280, 1855038645, 100034487540, 2697221086300, 36362467421275, 1960876019662560, 52870927596046560, 712777084536797285, 38437091637391006820, 1036375920040483589580, 13971856374727832955915

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OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..16.

MATHEMATICA

r = 5/2; 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}]] (* A195553, A195554 *)

Sqrt[a^2 + b^2] (* A195555 *)

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

CROSSREFS

Cf. A195500, A195554, A195555.

Sequence in context: A002554 A003383 A195575 * A142254 A159954 A079681

Adjacent sequences: A195550 A195551 A195552 * A195554 A195555 A195556

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Sep 21 2011

STATUS

approved