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 A371526 #4 Mar 27 2024 21:29:23
%S A371526 3,3,5,8,9,7,6,6,9,3,5,7,1,0,2,1,0,3,1,4,7,6,6,5,7,2,6,6,3,1,2,2,6,5,
%T A371526 8,0,4,8,5,4,6,1,0,4,0,2,1,3,7,3,4,8,9,4,1,8,0,5,4,6,6,6,6,6,6,1,2,9,
%U A371526 8,0,8,6,8,0,5,3,9,2,5,3,6,6,8,4,8,5,7,6,2,6,1,2,8,3,5,0,3,4,3,5,5,3,0,7,2,4,8,2,2,4,4,0,3,5,1,7,6,7,7,1
%N A371526 Decimal expansion of Product_{k>=2} (1 - 1/Lucas(k)).
%C A371526 Any two of the four constants {A337668, A337669, A371525, this} are algebraically independent over Q, while any three are not (Duverney et al., 2022).
%H A371526 Daniel Duverney, Carsten Elsner, Masanobu Kaneko, and Yohei Tachiya, <a href="https://doi.org/10.1007/s40993-022-00328-7">A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers</a>, Research in Number Theory, Vol. 8 (2022), Article 31; <a href="https://www2.math.kyushu-u.ac.jp/~mkaneko/papers/DEKT.pdf">alternative link</a>.
%H A371526 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>.
%H A371526 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dedekind_eta_function">Dedekind eta function</a>.
%F A371526 Equals Product_{k>=2} (1 - 1/A000032(k)).
%F A371526 Equals A371530 / (2*sqrt(5)).
%F A371526 Equals (phi^(1/4) / sqrt(5)) * eta(2*tau_0)^2 * eta(6*tau_0) / (eta(3*tau_0) * eta(4*tau_0)), where phi is the golden ratio (A001622), tau_0 = i*log(phi)/Pi, and i = sqrt(-1) (Duverney et al., 2022).
%e A371526 0.33589766935710210314766572663122658048546104021373...
%t A371526 With[{eta = DedekindEta, tau0 = Log[GoldenRatio]*I/Pi}, RealDigits[(Surd[GoldenRatio, 4] / Sqrt[5]) * eta[2*tau0]^2 * eta[6*tau0]/(eta[3*tau0] * eta[4*tau0]), 10, 120][[1]]]
%o A371526 (PARI) prodinf(k = 2, 1 - 1/(fibonacci(k-1) + fibonacci(k+1)))
%Y A371526 Cf. A000032, A001622, A002390, A337668, A337669, A371525, A371527, A371528, A371529, A371530.
%K A371526 nonn,cons
%O A371526 0,1
%A A371526 _Amiram Eldar_, Mar 26 2024