Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the High Water Mark Convergents of Champernowne's Constant in Base
  Ten   In this paper we show that numerous patterns exist in the properties of the
convergents formed by truncating the Continued Fraction Expansion (CFE) of the
Champernowne Constant in base 10 (C10) immediately before the High Water Marks
(HWMs). From these patterns, we have formulated conjectures that may be used to
predict the first position in C10 that is incorrect as calculated by the
convergent, the error of the convergent, the denominator of the convergent, and
the number of digits of C10 that are required to give the correct numerator of
the convergent. The numerator and denominator then provide a very efficient
method for calculating the CFE coefficients. In addition, we have formulated a
conjecture that predicts the exact length in decimal digits of each of the HWM
coefficients of C10 for HWM numbers greater than 3. Furthermore, it is
conjectured that the lengths of certain other large coefficients that appear in
the CFE of C10 are related to the lengths of the HWMs and a formula is given
for this relationship. We designate these other large coefficients 2nd
Generation HWMs, or Child HMWs. It is shown that 3rd, 4th, etc., Generation
HWMs also exist. A conjecture regarding the structure and exact length of the
denominators of the 2nd Generation HWM Convergents is presented. Finally, a
table is presented that shows the Coefficient Numbers and the lengths of the
3rd and 4th Generation coefficients up to but not including HWM number 12.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: hep-ph