

A138371


Count of postperiod decimal digits up to which the rounded nth convergent to A058265 agrees with the exact value.


1



0, 1, 2, 5, 8, 7, 10, 11, 10, 12, 15, 17, 17, 17, 20, 21, 22, 23, 25, 26, 28, 30, 29, 30, 31, 31, 32, 32, 34, 35, 35, 36, 36, 38, 40, 40, 42, 42, 42, 43, 44, 43, 45, 46, 47, 47, 49, 52, 51, 52, 54, 54, 55, 57, 59, 59, 60, 60, 60, 61, 61, 62, 62, 64, 64, 66, 67, 69, 71, 73, 74
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OFFSET

1,3


COMMENTS

This is a measure of the quality of the nth convergent to the tribonacci constant A058265 if the convergent and the exact value are compared rounded to an increasing number of digits. The sequence of rounded values of A058265 is 2, 1.8, 1.84, 1.839, 1.8393, 1.83929, 1.839287, 1.8392868, etc. The nth convergents are 2 (n=1), 11/6 (n=2), 46/25 (n=3), 103/56 (n=4), 31451/17105 (n=5) etc., each with associated rounded decimal expansions.
a(n) is the maximum number of postperiod digits of the two expansions if compared at the same level of rounding. Counting only postperiod digits (which is one less than the full number of decimal digits) is just a convention taken from A084407.


LINKS

Table of n, a(n) for n=1..71.


EXAMPLE

For n=4, the 4th convergent is 103/56 = 1.83928571..., with a sequence of rounded representations 2, 1.8, 1.84, 1.839, 1.8393, 1.83929, 1.839286, 1.8392857 etc.
Rounded to 1, 2, 3, 4 or 5 postperiod decimal digits, this is the same as the rounded version of the exact value, but disagrees if both are rounded to 6 decimal digits, where 1.839287 <> 1.839286.
So a(n=4) = 5 (digits), the maximum rounding level with agreement.


CROSSREFS

Cf. A138335, A138336, A138337, A138339, A138343, A138366, A138367, A138369, A138370.
Sequence in context: A057929 A154127 A250206 * A140053 A103311 A019824
Adjacent sequences: A138368 A138369 A138370 * A138372 A138373 A138374


KEYWORD

base,nonn


AUTHOR

Artur Jasinski, Mar 17 2008


EXTENSIONS

Definition and values replaced as defined via continued fractions by R. J. Mathar, Oct 01 2009


STATUS

approved



