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(Numerator of n-th convergent to Pi having an even numerator)/2.
0

%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