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Shallit Constant

Define $f(x_1,x_2,\ldots,x_n)$ with $x_i$ Positive as

f(x_1, x_2, \ldots, x_n)\equiv \sum_{i=1}^n x_i+\sum_{1\leq i\leq k\leq n} \prod_{j=i}^k {1\over x_j}.


\min f = 3n - C + o(1)

as $n$ increases, where the Shallit constant is

C = 1.369451403937\dots

(Shallit 1995). In their solution, Grosjean and De Meyer (quoted in Shallit 1995) reduced the complexity of the problem.


MacLeod, A.

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.

© 1996-9 Eric W. Weisstein