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).

number pattern | zerofree