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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the speed of convergence of the nearest integer continued fraction
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by H. Jager PDF
Math. Comp. 39 (1982), 555-558 Request permission


Let ${p_n}/{q_n}$ and ${A_n}/{B_n}$ denote the convergents of, respectively, the regular and the nearest integer continued fraction expansion of the irrational number x. There exists a function $k(n)$ such that ${A_n}/{B_n} = {p_{k(n)}}/{q_{k(n)}}$. Adams proved that for almost all x one has $\lim k(n)/n = \log 2/\log G$, $G = \frac {1}{2}(1 + \sqrt 5 )$. Here we present a shorter proof of this result, based on a simple expression for $k(n)$ and the ergodicity of the shift operator, connected with the nearest integer continued fraction.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 555-558
  • MSC: Primary 10K10
  • DOI:
  • MathSciNet review: 669647