Shallit Constant
Define 
with 
Positive as
Then
as
increases, where the Shallit constant is
(Shallit 1995). In their solution, Grosjean and De Meyer (quoted in Shallit 1995) reduced the complexity of the problem.
References
MacLeod, A. http://www.mathsoft.com/asolve/constant/shapiro/macleod.html. Shallit, J. Solution by C. C. Grosjean and H. E. De Meyer. ``A Minimization Problem.'' Problem 94-15 in SIAM Review 37, 451-458, 1995.
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