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.
%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