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 , 1, ... are 2, 64037, 6634003367, 666334000333667, ... (OEIS A052427). Primes occur for , 1, 7, 133, ... (OEIS A051832) with no others  (Weisstein, pers. comm., 2002), corresponding to 2, 64037, 66666663333334000000033333336666667, ... (OEIS A051833).

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."