A195538 - OEIS

%I #15 Dec 07 2016 10:33:26

%S 5,12,145,420,4901,14280,166465,485112,5654885,16479540,192099601,

%T 559819260,6525731525,19017375312,221682772225,646030941360,

%U 7530688524101,21946034630940,255821727047185,745519146510612,8690408031080165

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

%C See A195500 for a discussion and references.

%C Conjecture: a(n) = 35*a(n-2) - 35*a(n-4) + a(n-6) with bisections A098602 and A076218. - _R. J. Mathar_, Sep 21 2011

%t r = Sqrt[8]; z = 24;

%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}]]  (* A195538, A195539 *)

%t Sqrt[a^2 + b^2] (* A195540 *)

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

%Y Cf. A195500, A195539, A195540.

%K nonn,frac

%O 1,1

%A _Clark Kimberling_, Sep 20 2011