Here, I calculated a sequence of random Fibonacci numbers to approximate Viswanath’s constant \(e^{\gamma_f}\). Below is a Jupyter notbook I used for calculation and plotting. I had time to compute over \(13.5\) million numbers and found \(e^{\gamma_f}\) within \(0.0084\,\%\) error. My final approximation was \(e^{\gamma_f} \approx 1.1320836316\). If you have \(1.6\) GB free space on your disk you can download the full list of my computed random Fibonacci numbers with additional information.

Here is the convergence plot in higher resolution: