This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A195538 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(8). 4

%I

%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; z = 24;

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

%t 1]] &)[({2 #1[] #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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 15:10 EST 2019. Contains 329999 sequences. (Running on oeis4.)