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

2,2

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.

Links

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

Example

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

Crossrefs

Cf. A002485, A002486, A000796.

Sequence in context: A062886 A319585 A133452 * A251364 A229791 A189293

Adjacent sequences: A356662 A356663 A356664 * A356666 A356667 A356668

Keyword

nonn,base,easy

Author

Daniel Mondot, Aug 21 2022

Status

approved