The original article, by Thomas Oléron Evans [0], does something similar. I made a graph of it here. It's a heuristic estimate of the expected number of integers that satisfy the property for bases (2..b), as a function of b.
As the author writes, for b <= 4, the expected number diverges to +infinity. For b = 5, the expected number is less than one, and quickly decreases. So, the conjecture is that there is no satisfying solution for b >= 6.
https://i.imgur.com/3h8GSIp.png
https://gist.github.com/anonymous/9f71926313e6ee5c595c
As the author writes, for b <= 4, the expected number diverges to +infinity. For b = 5, the expected number is less than one, and quickly decreases. So, the conjecture is that there is no satisfying solution for b >= 6.
[0] http://www.mathistopheles.co.uk/maths/covering-all-the-bases...