cp's OEIS Frontend

A033089 Incrementally largest terms in the continued fraction for Pi.

%I A033089 #54 Feb 16 2025 08:32:36
%S A033089 3,7,15,292,436,20776,78629,179136,528210,12996958,878783625,
%T A033089 5408240597,5916686112,9448623833,9787547328,52662113289
%N A033089 Incrementally largest terms in the continued fraction for Pi.
%C A033089 There is no larger term in the first 15000000000 terms of the c.f. - _Eric W. Weisstein_, Jul 27 2013
%C A033089 There is no larger term in the first 30000000000 terms of the c.f. - _Syed Fahad_, Apr 27 2021
%H A033089 Syed Fahad, <a href="https://drive.google.com/drive/folders/1--Qh9Xxq1i6oeHnTXzKrQ9FoguHreBKy">30 billion terms of the simple continued fraction of Pi</a>
%H A033089 E. Fontich, C. Simó, and A. Vieiro, <a href="https://doi.org/10.1134/S1560354718060011">On the "hidden" harmonics associated to best approximants due to quasiperiodicity in splitting phenomena</a>, Regular and Chaotic Dynamics (2018), Pleiades Publishing, Vol. 23, Issue 6, 638-653.
%H A033089 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pi.html">Pi</a>
%H A033089 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>
%H A033089 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%t A033089 c = ContinuedFraction[ Pi, 10^7 ]; a = 0; i = 1; Do[ While[ c[ [ i ] ] <= a, i++ ]; a = c[ [ i ] ]; Print[ a ], {n, 1, 11} ]
%Y A033089 Apart from initial term, same as A007541.
%Y A033089 Cf. A033090 (indices), A000796, A001203.
%K A033089 nonn,hard
%O A033089 1,1
%A A033089 _Eric W. Weisstein_, _Bill Gosper_
%E A033089 Checked by _Hans Havermann_, Aug 07 2010
%E A033089 a(12) from _Eric W. Weisstein_, Dec 08 2010
%E A033089 a(13) from _Eric W. Weisstein_, Sep 16 2011
%E A033089 a(14) from _Eric W. Weisstein_, Sep 17 2011
%E A033089 a(15) from _Eric W. Weisstein_, Jul 18 2013
%E A033089 a(16) from _Syed Fahad_, Apr 27 2021