login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195544 Denominators a(n) of Pythagorean approximations b(n)/a(n) to Pi. 4

%I #12 Dec 07 2016 10:33:45

%S 12,52,315,1044,3296,20919,217620,450296,125510644,138980066871,

%T 289898680472,3593636117787,34812833117460,1934468176818608,

%U 1244148342635075,86081645453428848,8659539839551787053788,138771143651019468539176

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

%C See A195500 for a discussion and references.

%t r = Pi; z = 21;

%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}]] (* A195544, A195545 *)

%t Sqrt[a^2 + b^2] (* A195546 *)

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

%Y Cf. A195500, A195545, A195546.

%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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)