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 A052427 Baxter-Hickerson numbers. 3
 2, 64037, 6634003367, 666334000333667, 66663334000033336667, 6666633334000003333366667, 666666333334000000333333666667, 66666663333334000000033333336666667 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 25 07:07 EDT 2024. Contains 371964 sequences. (Running on oeis4.)