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Search: id:A059101
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| A059101 |
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Number of terms of the fractional part of A001203 for which the geometric mean produces increasingly better approximations to Khinchin's constant. |
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+0
1
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| 1, 3, 7, 8, 9, 10, 11, 15, 16, 17, 97, 100, 103, 117, 976, 32307, 32760, 32787, 60508, 60601, 60663, 187154, 230084, 1120375, 1146529, 2211732, 4497058
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next term > 180000000.
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LINKS
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H. Havermann, Simple Continued Fraction for Pi
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FORMULA
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p = Rest[{A001203}]; q = N[1, 100]; r = p[[1]] + 1; t = {}; Do[q = q*p[[i]]; g = q^(1/i) - Khinchin; If[Abs[g] < r, r = Abs[g]; t = Append[t, i]], {i, 1, Length[p]}]; t
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EXAMPLE
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The geometric mean of 17 terms (Khinchin + 0.00752006) is not bettered until we calculate the geometric mean of 97 terms (Khinchin - 0.00326655).
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CROSSREFS
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Cf. A001203, A048613.
Adjacent sequences: A059098 A059099 A059100 this_sequence A059102 A059103 A059104
Sequence in context: A064540 A103560 A011398 this_sequence A091679 A116034 A122987
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KEYWORD
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cofr,nonn
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AUTHOR
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Hans Havermann (pxp(AT)rogers.com), Feb 13 2001
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