Continued fraction expansion of algebraic numbers
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Every irrational x in (0,1) determines uniquely an infinite sequence of positive integers by means of its continued fraction expansion. Richtmyer in 1951 conjectured that algebraic irrationals may have a paucity of large partial denominators. The conjecture was studied in numerical tests. The numerical work yielded a very strange result for one value of x. The present paper reports further tests for this value. It was found that the previous anomalous value was accidental, and resulted from having stopped the expansion at 725 terms; other stopping points gave quite reasonable values. 4 tables. (RWR)
[1] K. F. Roth,et al. Rational approximations to algebraic numbers , 1955 .
[2] R. D. Richtmyer,et al. Continued fraction expansions of algebraic numbers , 1962 .
[3] R. D. Richtmyer. THE EVALUATION OF DEFINITE INTEGRALS, AND A QUASI-MONTE-CARLO METHOD BASED ON THE PROPERTIES OF ALGEBRAIC NUMBERS , 1951 .