

A138370


Count of postperiod decimal digits up to which the rounded nth convergent to 4*sin(2*Pi/5) agrees with the exact value.


5



2, 3, 4, 5, 5, 6, 6, 8, 9, 10, 11, 12, 12, 13, 14, 15, 15, 17, 18, 17, 19, 21, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 33, 34, 35, 36, 37, 38, 38, 40, 41, 42, 41, 42, 43, 45, 44, 46, 44, 47, 49, 49, 50, 52, 53, 54, 55, 57, 59, 60, 61, 63, 62, 65, 67, 67, 68, 70, 69, 70, 70, 71
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

The computation of A138369 is repeated for 4*sin(2*Pi/5) = sqrt(2)*sqrt(5+sqrt(5))
= 3.80422606518061.. = 4*A019881.
The convergents are 19/5 (n=2), 175/46 (n=3), 544/143 (n=4), 719/189 (n=5), 2701/710 (n=6) etc.


LINKS

Table of n, a(n) for n=2..73.


EXAMPLE

a(6)=5 because 2701/710 = 3.80422535... agrees with 3.8042260651.. if both are rounded up to 5 decimal digits (3.80423 = 3.80423), but disagrees at the level of rounding to 6 decimal digits (3.804226 <> 3.804225) or more.


CROSSREFS

Cf. A138335, A138336, A138337, A138339, A138343, A138366, A138367, A138369.
Sequence in context: A063882 A097873 A005375 * A125051 A064067 A202306
Adjacent sequences: A138367 A138368 A138369 * A138371 A138372 A138373


KEYWORD

base,less,nonn


AUTHOR

Artur Jasinski, Mar 17 2008


EXTENSIONS

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


STATUS

approved



