A052427 Baxter-Hickerson numbers.

2, 64037, 6634003367, 666334000333667, 66663334000033336667, 6666633334000003333366667, 666666333334000000333333666667, 66666663333334000000033333336666667

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn

Comments

From Amiram Eldar, Nov 23 2020: (Start)

Named after Lew Baxter and Dean Hickerson.

Pegg (1999) conjectured that the sequence of zeroless cubes (A052045) is finite. On April 19, 1999, Hickerson gave the counterexample: if n == 2 (mod 3) and n >= 5, then the cube of (2*10^(5*n) - 10^(4*n) + 17*10^(3*n-1) + 10^(2*n) + 10^n - 2)/3 is zeroless. Three days later, Baxter gave a simpler variation which is valid for all n>=0 and is given in the Formula section. (End)

References

• Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005. See p. 109.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..200
• Lew Baxter, Cubes lacking zeros, sci.math newsgroup, April 22, 1999.
• Ed Pegg, Jr., Cube conjecture, sci.math newsgroup, April 18, 1999.
• Ed Pegg, Jr., Fun with Numbers, mathpuzzle websize.
• Eric Weisstein's World of Mathematics, Baxter-Hickerson Function.

Crossrefs

Subsequence of A052044.

Cf. A016789, A051832, A051833, A052045.

Programs

Maple

a(0) = 2, and 2^3 = 8 is zeroless.
a(1) = 64037, and 64037^3 = 262598918898653 is zeroless.

Mathematica

a[n_] := (2*10^(5*n) - 10^(4*n) + 2*10^(3*n) + 10^(2*n) + 10^n + 1)/3; Array[a, 10, 0] (* Amiram Eldar, Nov 23 2020 *)

Formula

a(n) = (2*10^(5*n) - 10^(4*n) + 2*10^(3*n) + 10^(2*n) + 10^n + 1)/3 (Baxter, 1999). - Amiram Eldar, Nov 23 2020

Extensions

Offset changed to 0 by Amiram Eldar, Nov 23 2020