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A138372
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Count of post-period decimal digits up to which the rounded n-th convergent to A103814 agrees with the exact value.
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0
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1, 3, 3, 4, 3, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 12, 13, 13, 14, 16, 16, 18, 21, 23, 23, 24, 26, 27, 27, 29, 29, 30, 30, 31, 32, 34, 37, 36, 39, 40, 41, 42, 43, 43, 46, 47, 48, 48, 49, 50, 50, 52, 53, 54, 55, 56, 56, 58, 58, 59, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 73, 73, 75
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is a measure of the quality of the n-th convergent to the Pentanacii constant
A103814 if the convergent and the exact value are compared rounded to an increasing
number of digits. The sequence of rounded values of A103814 is
2, 2.0, 1.97, 1.966, 1.9659, 1.96595, 1.965948, 1.9659482 etc. The n-th convergents
are 2 (n=1), 57/29 (n=2), 116/59 (n=3), 173/88 (n=4), 462/235 (n=5) etc, 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
| For n=5, the 5th convergent is 462/235 = 1.96595744.., with a sequence of rounded
representations 2, 2.0, 1.97, 1.966, 1.9660, 1.96596, 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 1.9659 <> 1.9660.
So a(n=5)= 3 (digits), the maximum rounding level with agreement.
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CROSSREFS
| Cf. A138335 - A138339, A138343, A138366, A138367, A138369 - A138371, A138373 - A138374.
Sequence in context: A096139 A175928 A161357 * A123708 A102302 A130896
Adjacent sequences: A138369 A138370 A138371 * A138373 A138374 A138375
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KEYWORD
| base,nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Mar 17 2008
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EXTENSIONS
| Definition and values replaced as defined via continued fractions - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 01 2009
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