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 A371527 #4 Mar 27 2024 21:29:37
%S A371527 1,1,3,8,7,3,4,8,6,1,7,0,7,1,9,6,2,1,8,0,9,6,8,9,5,0,8,5,7,4,2,0,4,3,
%T A371527 1,8,7,6,3,7,8,8,8,9,4,7,9,1,5,7,3,2,5,1,3,7,4,4,1,3,4,4,2,4,2,6,4,9,
%U A371527 2,2,8,1,6,7,4,2,2,2,2,2,6,7,4,0,0,7,8,6,2,3,9,3,3,8,4,0,9,2,1,7,6,4,4,3,9
%N A371527 Decimal expansion of Product_{k>=2} (1 + (-1)^k/Fibonacci(k)).
%H A371527 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 A371527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>.
%H A371527 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dedekind_eta_function">Dedekind eta function</a>.
%F A371527 Equals Product_{k>=2} (1 + (-1)^k/A000045(k)).
%F A371527 Equals 6 * A337669.
%F A371527 Equals 2 * sqrt(5) * phi^(5/4) * eta(tau_0)^3 * eta(4*tau_0) / eta(2*tau_0)^2, where phi is the golden ratio (A001622), tau_0 = i*log(phi)/Pi, and i = sqrt(-1) (Duverney et al., 2022).
%e A371527 1.13873486170719621809689508574204318763788894791573...
%t A371527 With[{eta = DedekindEta, tau0 = Log[GoldenRatio]*I/Pi}, RealDigits[2 * Sqrt[5] * Surd[GoldenRatio^5, 4] * eta[tau0]^3 * eta[4*tau0]/eta[2*tau0]^2, 10, 120][[1]]]
%o A371527 (PARI) prodinf(k = 2, 1 + (-1)^k/fibonacci(k))
%Y A371527 Cf. A000045, A001622, A002390, A337668, A337669, A371525, A371526, A371528, A371529, A371530.
%K A371527 nonn,cons
%O A371527 1,3
%A A371527 _Amiram Eldar_, Mar 26 2024