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Baxter-Hickerson Function

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In April 1999, Ed Pegg conjectured on sci.math that there were only finitely many zerofree cubes, to which D. Hickerson responded with a counterexample. A few days later, Lew Baxter posted the slightly simpler example

f(n)=1/3(2·10^(5n)-10^(4n)+2·10^(3n)+10^(2n)+10^n+1),

which produces numbers whose cubes lack zeros. The first few terms for n=0, 1, ... are 2, 64037, 6634003367, 666334000333667, ... (OEIS A052427). Primes occur for n=0, 1, 7, 133, ... (OEIS A051832) with no others <=650 (Weisstein, pers. comm., 2002), corresponding to 2, 64037, 66666663333334000000033333336666667, ... (OEIS A051833).

See also

Number Pattern, Zerofree

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References

Pegg, E. Jr. "Fun with Numbers." http://www.mathpuzzle.com/numbers.html.Sloane, N. J. A. Sequences A051832, A051833, and A052427 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Baxter-Hickerson Function

Cite this as:

Weisstein, Eric W. "Baxter-Hickerson Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Baxter-HickersonFunction.html

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