

A195538


Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(8).


4



5, 12, 145, 420, 4901, 14280, 166465, 485112, 5654885, 16479540, 192099601, 559819260, 6525731525, 19017375312, 221682772225, 646030941360, 7530688524101, 21946034630940, 255821727047185, 745519146510612, 8690408031080165
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OFFSET

1,1


COMMENTS

See A195500 for a discussion and references.
Conjecture: a(n) = 35*a(n2)  35*a(n4) + a(n6) with bisections A098602 and A076218.  R. J. Mathar, Sep 21 2011


LINKS

Table of n, a(n) for n=1..21.


MATHEMATICA

r = Sqrt[8]; 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}]] (* A195538, A195539 *)
Sqrt[a^2 + b^2] (* A195540 *)
(* Peter J. C. Moses, Sep 02 2011 *)


CROSSREFS

Cf. A195500, A195539, A195540.
Sequence in context: A096314 A332466 A323565 * A330218 A047658 A290804
Adjacent sequences: A195535 A195536 A195537 * A195539 A195540 A195541


KEYWORD

nonn,frac


AUTHOR

Clark Kimberling, Sep 20 2011


STATUS

approved



