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%I #9 Mar 08 2023 09:51:26
%S 11,52174,573204,122925461,534483448,3083975227,2685575996367,
%T 214112296674652,131226315167691099699,396325638628212603442,
%U 5947531272548328355975,118554299812338354516058
%N (Numerator of n-th convergent to Pi having an even numerator)/2.
%C Abs[Cos[a(n)]] approaches 0; Abs[Sin[a(n)]] approaches 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Convergent.html">Convergent</a>.
%e a(1) = 11 because the first convergent of Pi with an even numerator is 22/7.
%t Select[Table[1/2*Numerator[FromContinuedFraction[ContinuedFraction[Pi, k][[Range[1, k]]]]], {k, 1, 60}], IntegerQ]
%Y Cf. A000796, A002485.
%K base,nonn
%O 1,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Feb 22 2005
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