Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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