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Baxter-Hickerson Function

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The Baxter-Hickerson function is the function

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

for nonnegative integer n. Its cubes f(n)^3 are zerofree.

Baxter (1999) posted the formula above after D. Hickerson gave a counterexample to E. Pegg, Jr.'s conjecture that only finitely many zerofree cubes existed. The discussion took place on sci.math in April 1999.

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 other such n<=650 found in the cited search (E. W. Weisstein, pers. comm., 2002), corresponding to 2, 64037, 66666663333334000000033333336666667, ... (OEIS A051833).

See also

Number Pattern, Zerofree

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References

Baxter, L. "Cubes Lacking Zeros." sci.math newsgroup posting. 22 Apr 1999. https://groups.google.com/g/sci.math/c/gX5a49ZCYrc/m/lTSZRKNdjZoJ.Pegg, E. Jr. "MathPuzzle: Fun with Numbers." Jun. 1, 2002. https://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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