A138370 Count of post-period decimal digits up to which the rounded n-th convergent to 4*sin(2*Pi/5) agrees with the exact value.

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

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