A195580 - OEIS

%I #11 Mar 11 2014 01:40:52

%S 4,600,2600,15996,2460800,10652800,65552004,10084355800,43655173800,

%T 268632095996,41325687609600,178898891577600,1100854263840004,

%U 169352657739783000,733127614029833000,4511300504584239996,694007150091943126400

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

%C See A195500 for a discussion and references.

%t r = 4/5; z = 18;

%t p[{f_, n_}] := (#1[[2]]/#1[[

%t       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[

%t          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[

%t      Array[FromContinuedFraction[

%t         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];

%t {a, b} = ({Denominator[#1], Numerator[#1]} &)[

%t   p[{r, z}]]  (* A195580, A195611 *)

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

%t (* _Peter J. C. Moses_, Sep 02 2011 *)

%Y Cf. A195500, A195611, A195612.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 21 2011