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

Author

Artur Jasinski, Mar 17 2008

Keywords

• base
• less
• nonn

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.

Examples

			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.

Extensions

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