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MathGroup Archive 2000

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Maxim Rytin / Champernowne

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22935] Maxim Rytin / Champernowne
  • From: Hans Havermann <haver at total.net>
  • Date: Thu, 6 Apr 2000 02:04:52 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Maxim Rytin is the author of the delightful "Champernowne Constant and Its
Continued Fraction Expansion"
<http://www.mathsource.com/Content/Applications/Mathematics/0210-542>...
I've used this notebook to compute cf3[\[Xi]\_7] yielding 13522 terms of
the continued fraction. I thought I might have had enough RAM for an
attempt at cf3[\[Xi]\_8] but I'm getting "overflow occurred" fairly early
in the computation. Don't really understand the math well enough to know if
this is fixable.

Does anybody here know the author?


Defined as the decimal number having after the decimal point the digits
of consecutive natural numbers beginning with one: 0.12345678910111213
..., the simple continued fraction expansion of Champernowne is [0; 8,
9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15,
457540111391031076483646628242956118599603939710457555000662004393090262
659256314937953207747128656313864120937550355209460718308998457580146986
3148833592141783010987, 6, ...].

Let the index of these terms be [0; 1, 2, 3, ...]. Here is a list of
{index, number of digits in term} where the number of digits in the term
exceeds 3:

        {4, 6}
        {18, 166}
        {40, 2504}
        {101, 140}
        {162, 33102}
        {246, 109}
        {357, 2468}
        {459, 136}
        {526, 411100}
        {638, 90}
        {820, 2423}
        {1051, 63}
        {1221, 33056}
        {1362, 95}
        {1515, 2458}
        {1627, 120}
        {1708, 4911098}
        {1850, 69}
        {2074, 2411}
        {2175, 4}
        {2309, 52}
        {2364, 4}
        {2528, 33005}
        {2798, 12}
        {3071, 2374}
        {3090, 4}
        {3160, 4}
        {3339, 38}
        {3569, 411044}
        {3653, 5}
        {3726, 84}
        {3916, 2419}
        {4141, 57}
        {4311, 33051}
        {4464, 97}
        {4615, 2457}
        {4745, 115}
        {4838, 57111096}
        {5002, 49}
        {5268, 2391}
        {5545, 31}
        {5810, 32985}
        {6229, 4}
        {6417, 2354}
        {6729, 18}
        {6871, 4}
        {6992, 410979}
        {7718, 2308}
        {8065, 4}
        {8469, 32939}
        {8777, 4}
        {9207, 2345}
        {9827, 4911032}
        {10034, 56}
        {10279, 4}
        {10292, 2393}
        {10559, 29}
        {10822, 32996}
        {11439, 2359}
        {11771, 26}
        {11781, 4}
        {12015, 411036}
        {12202, 72}
        {12345, 4}
        {12414, 2405}
        {12659, 45}
        {12869, 33041}
        {13054, 75}
        {13251, 2438}
        {13417, 101}
        {13522, X}

What is X?




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