A052427 Baxter-Hickerson numbers.

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

Offset

0,1

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.

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

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 *)

Crossrefs

Subsequence of A052044.

Cf. A016789, A051832, A051833, A052045.

Sequence in context: A059764 A285694 A306907 * A051833 A213619 A060895

Adjacent sequences: A052424 A052425 A052426 * A052428 A052429 A052430

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Offset changed to 0 by Amiram Eldar, Nov 23 2020

Status

approved