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How to calculate digits of numbers (Trott Constant) whose continued fraction representation is the same as the digits of its radix representation with Mathematica?

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  • 1
    $\begingroup$ "However, attempts to extend the number of digits have proved problematic." (from the Mathworld article) $\endgroup$ – Patrick Stevens Dec 24 '15 at 19:47
  • $\begingroup$ Have a look at this article. $\endgroup$ – J. M. is away Feb 16 '16 at 12:23
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WolframAlpha["trott constant", {{"ContinuedFraction", 1}, "Input"}, 
 PodStates -> {"ContinuedFraction__Fraction form"}]

(*
  HoldComplete[
    ContinuedFraction[
      0.108410151223111361511290811406415091122158090939091, 23
    ]
   ]
*)

You can sub in other numbers for the above 23

ContinuedFraction[0.108410151223111361511290811406415091122158090939091, 20]

(*{0, 9, 4, 2, 5, 1, 2, 2, 3, 1, 1, 1, 3, 6, 1, 5, 1, 1, 2, 17}*)
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