This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156019 #27 Jul 03 2022 09:06:49
%S A156019 3,15,73,1,2,3,7,1,2,2,1,2,1,3,1,2,6,1,1,3,1,6,1,1,3,1,1,3,1,3,1,1,2,
%T A156019 6,1,2,3,1,1,1,45,22,2,1,1,24,2,1,2,1,2,4,2,8,5,1,1,1,2,7,1,3,1,7,4,7,
%U A156019 3,3,9,9,1,18,3,15,1,1,1,1,1,2,3,1,1,1,1
%N A156019 Numerators in an infinite sum for Pi.
%C A156019 For k >= 0, define Q(k) = A002485(2k)/A002486(2k) (convergents to Pi that are less than Pi), so Pi = Sum_{k>=1} (Q(k) - Q(k-1)). Then a(n) is the numerator of Q(n) - Q(n-1).
%F A156019 a(n) = numerator(A002485(2n)/A002486(2n) - A002485(2n-2)/A002486(2n-2)).
%e A156019 a(2) = 15 since A002485(4)/A002486(4) = 333/106, A002485(2)/A002486(2) = 3/1, and 333/106 - 3/1 = 15/106 (see table below).
%e A156019 Pi = 3/1 + 15/106 + 73/877203 + 1/2195225334 + 2/17599271777 + 3/360950005720 + 7/17348726394920 + ....
%e A156019 .
%e A156019 n Q(n) = A002485(2n)/A002486(2n) Q(n) - Q(n-1) a(n)
%e A156019 - ------------------------------ ------------- ----
%e A156019 0 0/1 = 0 - -
%e A156019 1 3/1 = 3 3/1 3
%e A156019 2 333/106 = 3.1415094339... 15/106 15
%e A156019 3 103993/33102 = 3.1415926530... 73/877203 73
%Y A156019 Cf. A000796, A002485, A002486, A156020 (denominators).
%K A156019 nonn,frac
%O A156019 1,1
%A A156019 _Gary W. Adamson_ and _Alexander R. Povolotsky_, Feb 01 2009
%E A156019 More terms from _Alexander R. Povolotsky_, Sep 01 2009
%E A156019 Edited by _Jon E. Schoenfield_, Jan 04 2022
%E A156019 More terms from _Jinyuan Wang_, Jun 29 2022