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%I #7 Mar 19 2013 10:32:28
%S 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,
%T 26,27,29,30,31,33,33,34,35,36,37,38,38,40,41,42,41,42,43,45,44,46,44,
%U 47,49,49,50,52,53,54,55,57,59,60,61,63,62,65,67,67,68,70,69,70,70,71
%N 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.
%C The computation of A138369 is repeated for 4*sin(2*Pi/5) = sqrt(2)*sqrt(5+sqrt(5))
%C = 3.80422606518061.. = 4*A019881.
%C The convergents are 19/5 (n=2), 175/46 (n=3), 544/143 (n=4), 719/189 (n=5), 2701/710 (n=6) etc.
%e 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.
%Y Cf. A138335, A138336, A138337, A138339, A138343, A138366, A138367, A138369.
%K base,less,nonn
%O 2,1
%A _Artur Jasinski_, Mar 17 2008
%E Definition and values replaced as defined via continued fractions - _R. J. Mathar_, Oct 01 2009
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