A356665 Number of correct decimal digits of the approximation of Pi obtained from the continued fraction convergents A002485(n)/A002486(n).

1, 3, 5, 7, 10, 10, 10, 10, 12, 11, 13, 13, 15, 16, 16, 17, 18, 18, 19, 20, 22, 24, 25, 25, 26, 28, 30, 31, 31, 33, 34, 35, 38, 40, 41, 41, 42, 43, 45, 46, 46, 47, 48, 50, 51, 52, 52, 54, 55, 56, 56, 57, 57, 59, 60, 60, 61, 61, 62, 61, 63, 65, 64

Offset: 2

Author

Daniel Mondot, Aug 21 2022

Keywords

• nonn
• base
• easy

Comments

For most terms the number of correct digits is equal to or slightly less than the sum of the number of digits of the numerator and the denominator.

But for some pairs, the number of correct digits exceeds that sum. For example, a(5) = 7 digits is 1 more than length("355") + length("113") = 6.

Examples

			For n=5, A002485(5)/A002486(5) = 355/113 = 3.1415929..., 7 correct decimal digits of Pi. So a(5) = 7.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A002485, A002486, A000796.