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Hofstadter’s Conjecture for \(\alpha = \sqrt 2 - 1\)

  • Russell Jay Hendel

Abstract

The goal of this paper is to generalize the concepts and methods used in the study of Hofstadter’s extraction conjecture begun in [2] and [5]. Let α, 0 < α < 1, be irrational, let x = x(α) be the infinite string whose n-th element is “c” or “d” depending on whether [(n + l)α] − [na] equals 0 or 1 respectively, with [z] denoting the greatest integer function. For integer m ≥ 0 define s m , x m by
$$ x = {s_m}{x_m}, L\left( {{s_m}} \right) = m $$
(1)
with L(s) denoting the length of the string s.

Keywords

Induction Hypothesis Initial Segment Induction Assumption Empty String Recursive Definition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Russell Jay Hendel

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