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 A219015 #16 Aug 05 2025 12:19:44
%S A219015 29,45232349,189482250299273866821980904657123150749
%N A219015 Denominators in a product expansion for sqrt(2).
%C A219015 a(3) has 192 digits and a(4) has 957 digits.
%C A219015 The product expansion in question is sqrt(2) = Product_{n = 0..infinity} (1 + 2*A219014(n)/A219015(n)) = (1 + 2*6/29)*(1 + 2*6726/45232349)*....
%H A219015 Alois P. Heinz, <a href="/A219015/b219015.txt">Table of n, a(n) for n = 0..4</a>
%F A219015 a(n) = Pell(5^(n+1))/Pell(5^n), where Pell(n) = A000129(n).
%F A219015 Recurrence equation: a(n+1) = 5/2*(a(n)^4 - a(n)^2)*sqrt(4*a(n) + 5) + a(n)^5 + 15/2*a(n)^4 - 25/2*a(n)^2 + 5 with initial condition a(0) = 29.
%t A219015 Table[Fibonacci[5^(n+1),2]/Fibonacci[5^n,2], {n,0,5}] (* _G. C. Greubel_, Feb 02 2018 *)
%Y A219015 Cf. A000129, A219011, A219013, A219014.
%K A219015 nonn,easy,bref
%O A219015 0,1
%A A219015 _Peter Bala_, Nov 09 2012