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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=1.369451403993...
(3)

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

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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. 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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