Baxter-Hickerson Function

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


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

Explore with Wolfram|Alpha


Pegg, E. Jr. "Fun with Numbers.", 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 Web Resource.

Subject classifications