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Shallit Constant

The Shallit constant arises from minimizing the function f(x_1,x_2,...,x_n), defined for a positive integer n and positive real numbers x_i by

f(x_1,x_2,...,x_n)=sum_(i=1)^nx_i+sum_(1<=i<=k<=n)product_(j=i)^k1/(x_j).
(1)

Then

minf=3n-C+o(1)
(2)

as n->infty (Sadov 2021), where the Shallit constant is

C=1.369451403993770058435527924206...
(3)

(OEIS A086276; Sadov 2021). In their solution, Grosjean and De Meyer (quoted in Shallit 1995) reduced the complexity of the problem.

Jeffrey Shallit pointing to the decimal value of his constant at the University of Waterloo

Jeffrey Shallit points to the decimal value of his constant in the photograph above (photo by Anna Lubiw).

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References

Finch, S. R. "Shapiro-Drinfeld Constant." §3.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 208-211, 2003.Sadov, S. Yu. "On Shallit's Minimization Problem." Math. Notes 110, 375-392, 2021. https://doi.org/10.1134/S0001434621090078.Shallit, J. "Home Page of Jeffrey O. Shallit." https://cs.uwaterloo.ca/~shallit/.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.Sloane, N. J. A. Sequence A086276 in "The On-Line Encyclopedia of Integer Sequences."

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Shallit Constant

Cite this as:

Weisstein, Eric W. "Shallit Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ShallitConstant.html

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