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 A337668 #19 Mar 26 2024 09:39:34
%S A337668 1,3,1,5,0,9,6,6,6,5,7,7,8,4,1,8,4,3,6,7,6,1,2,4,3,3,3,7,0,6,2,6,6,5,
%T A337668 8,9,3,2,1,9,0,1,9,9,5,4,3,1,6,4,2,8,4,7,0,1,3,5,4,1,0,0,7,4,7,1,5,7,
%U A337668 6,9,8,0,4,6,0,2,7,6,1,1,8,0,9,1,1,8,2,4
%N A337668 Decimal expansion of Product_{n>=1} (1+1/Fibonacci(n)).
%H A337668 Daniel Duverney and Yohei Tachiya, <a href="https://doi.org/10.3792/pjaa.97.006">Algebraic independence of certain infinite products involving the Fibonacci numbers</a>, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 97, No. 5 (2021), pp. 29-31; <a href="https://arxiv.org/abs/2009.06250">arXiv preprint</a>, arXiv:2009.06250 [math.NT], 2020.
%H A337668 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 A337668 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>.
%H A337668 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>.
%H A337668 Wikipedia, <a href="https://en.wikipedia.org/wiki/Theta_function">Theta function</a>.
%F A337668 Equals 2 * b^(-5/4) * theta_2(b)/theta_4(b^4), where theta_i are the Jacobi theta functions and b = 1/phi = A094214 (Duverney and Tachiya, 2021). - _Amiram Eldar_, May 27 2021
%F A337668 Equals 4 * phi^(5/4) * eta(4*tau_0) / eta(tau_0), where phi is the golden ratio (A001622), tau_0 = i*log(phi)/Pi, and i = sqrt(-1) (Duverney et al., 2022). - _Amiram Eldar_, Mar 26 2024
%e A337668 13.15096665778418436761243337...
%t A337668 With[{b = 1/GoldenRatio}, RealDigits[2*b^(-5/4)*EllipticTheta[2, 0, b]/EllipticTheta[4, 0, b^4], 10, 100][[1]]] (* _Amiram Eldar_, May 27 2021 *)
%o A337668 (PARI) prodinf(n=1, 1+1/fibonacci(n))
%Y A337668 Cf. A000045, A001622, A094214, A337669.
%K A337668 nonn,cons
%O A337668 2,2
%A A337668 _Michel Marcus_, Sep 15 2020
%E A337668 More terms from _Jinyuan Wang_, Sep 19 2020