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Search: id:A138374
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| A138374 |
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Count of post-period decimal digits up to which the rounded n-th convergent to 2^(1/3) agrees with the exact value. |
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+0
3
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| 1, 1, 2, 2, 3, 4, 4, 6, 6, 8, 6, 10, 10, 12, 13, 15, 16, 17, 16, 18, 19, 20, 21, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 35, 38, 39, 40, 39, 41, 42, 45, 46, 46, 47, 49, 51, 52, 52, 54, 56, 56, 57, 58, 58, 60, 61, 62, 63, 65, 64, 66, 68, 69, 69, 70, 70, 72, 74, 74, 75, 77, 79, 81
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This is a measure of the quality of the n-th convergent to the constant
A002580 if the convergent and the exact value are compared rounded to an increasing
number of digits. The sequence of rounded values of A002580 is
1, 1.3, 1.26, 1.260, 1.2599, 1.25992, 1.259921, 1.2599211 etc. The n-th convergents
are taken from A002352 and A002351, each with associated rounded decimal expansions.
a(n) is the maximum number of post-period digits of the two expansions
if compared at the same level of rounding.
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EXAMPLE
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For n=5, the 5th convergent is 63/50 = 1.26000000.., with a sequence of rounded
representations 1, 1.3, 1.26, 1.260, 1.2600, 1.26000, etc.
Rounded to 1, 2, or 3 post-period decimal digits, this is the same as the rounded version
of the exact value, but disagrees if both are rounded to 4 decimal digits, where 1.2599 <> 1.2600.
So a(n=5)= 3 (digits), the maximum rounding level with agreement.
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CROSSREFS
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Cf. A138335, A138336, A138337, A138338, A138339, A138343, A138366, A138367, A138369, A138370, A138371, A138372, A138373, A138375, A138376, A138377, A138378, A138378, A138379.
Sequence in context: A113967 A126246 A138369 this_sequence A029936 A114093 A077768
Adjacent sequences: A138371 A138372 A138373 this_sequence A138375 A138376 A138377
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KEYWORD
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base,nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Mar 17 2008
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EXTENSIONS
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Definition and values replaced as defined via continued fractions - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 01 2009
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