cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A195544 Denominators a(n) of Pythagorean approximations b(n)/a(n) to Pi.

This page as a plain text file.
%I A195544 #12 Dec 07 2016 10:33:45
%S A195544 12,52,315,1044,3296,20919,217620,450296,125510644,138980066871,
%T A195544 289898680472,3593636117787,34812833117460,1934468176818608,
%U A195544 1244148342635075,86081645453428848,8659539839551787053788,138771143651019468539176
%N A195544 Denominators a(n) of Pythagorean approximations b(n)/a(n) to Pi.
%C A195544 See A195500 for a discussion and references.
%t A195544 r = Pi; z = 21;
%t A195544 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195544       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195544          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195544      Array[FromContinuedFraction[
%t A195544         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195544 {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t A195544   p[{r, z}]]  (* A195544, A195545 *)
%t A195544 Sqrt[a^2 + b^2] (* A195546 *)
%t A195544 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195544 Cf. A195500, A195545, A195546.
%K A195544 nonn,frac
%O A195544 1,1
%A A195544 _Clark Kimberling_, Sep 20 2011