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.

A282496 'Somos expansion' of Pi: Pi=a(0)*sqrt(a(1)*sqrt(a(2)*sqrt(a(3)*sqrt(...)))). a(n)=floor(x(n)), x(n)=x(n-1)^2/a(n-1)^2, x(0)=Pi.

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%I A282496 #10 Feb 19 2017 14:04:48
%S A282496 3,1,1,1,2,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,2,2,1,1,2,1,1,1,1,3,1,2,1,3,
%T A282496 1,1,2,2,1,1,2,1,1,2,1,2,1,1,1,1,1,1,1,3,1,2,1,1,3,1,2,1,1,1,1,3,1,2,
%U A282496 1,1,1,2,1,3,1,1,1,1,1,1,1,1,3,1,1,2,1,3,1,1,1,1,1,3,1,1,2,1,1,3,1,1,3,1,2,1,1,1,1,1,2,1,1,1,1,3,1,2,2,1,1,1,1,2,1,3,1,1,1,1
%N A282496 'Somos expansion' of Pi: Pi=a(0)*sqrt(a(1)*sqrt(a(2)*sqrt(a(3)*sqrt(...)))). a(n)=floor(x(n)), x(n)=x(n-1)^2/a(n-1)^2, x(0)=Pi.
%C A282496 1<=a(n)<=3 for all n. Reasoning: for x>1 it follows that 1<x/floor(x)<2.
%H A282496 Yuriy Sibirmovsky, <a href="/A282496/b282496.txt">Table of n, a(n) for n = 0..1999</a>
%F A282496 Product_{k>=0} a(k)^(1/2^k) = Pi.
%e A282496 Integer part of Pi is 3. Integer part of Pi^2/9 is 1.
%t A282496 $MaxExtraPrecision = 1000;
%t A282496 x00 = Pi;
%t A282496 x0 = x00;
%t A282496 Nm = 130;
%t A282496 j = 1;
%t A282496 Res = Table[1, {j, 1, Nm}];
%t A282496 While[j < Nm, Res[[j]] = Floor[x0]; x0 = N[(x0/ Res[[j]])^2, 20000];
%t A282496   j++];
%t A282496 Res
%Y A282496 Cf. A000796 (digits), A100044 (Pi^2/9), A001203 (continued fraction), A276459 (another nested radical expansion).
%K A282496 nonn
%O A282496 0,1
%A A282496 _Yuriy Sibirmovsky_, Feb 16 2017