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Number of correct decimal digits of the approximation of Pi obtained from the continued fraction convergents A002485(n)/A002486(n).
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%I #34 Jan 01 2023 17:14:44

%S 1,3,5,7,10,10,10,10,12,11,13,13,15,16,16,17,18,18,19,20,22,24,25,25,

%T 26,28,30,31,31,33,34,35,38,40,41,41,42,43,45,46,46,47,48,50,51,52,52,

%U 54,55,56,56,57,57,59,60,60,61,61,62,61,63,65,64

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

%C 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.

%C 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.

%H Daniel Mondot, <a href="/A356665/b356665.txt">Table of n, a(n) for n = 2..10000</a>

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

%Y Cf. A002485, A002486, A000796.

%K nonn,base,easy

%O 2,2

%A _Daniel Mondot_, Aug 21 2022