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A033089 Incrementally largest terms in the continued fraction for Pi. 5

%I

%S 3,7,15,292,436,20776,78629,179136,528210,12996958,878783625,

%T 5408240597,5916686112,9448623833,9787547328,52662113289

%N Incrementally largest terms in the continued fraction for Pi.

%C There is no larger term in the first 15000000000 terms of the c.f. - _Eric W. Weisstein_, Jul 27 2013

%C There is no larger term in the first 30000000000 terms of the c.f. - _Syed Fahad_, Apr 27 2021

%H Syed Fahad, <a href="https://drive.google.com/drive/folders/1--Qh9Xxq1i6oeHnTXzKrQ9FoguHreBKy">30 billion terms of the simple continued fraction of Pi</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi.html">Pi</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>

%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>

%t c = ContinuedFraction[ Pi, 10^7 ]; a = 0; i = 1; Do[ While[ c[ [ i ] ] <= a, i++ ]; a = c[ [ i ] ]; Print[ a ], {n, 1, 11} ]

%Y Apart from initial term, same as A007541.

%Y Cf. A033090 (indices), A000796, A001203.

%K nonn,hard,changed

%O 1,1

%A _Eric W. Weisstein_, _Bill Gosper_

%E Checked by _Hans Havermann_, Aug 07 2010

%E a(12) from _Eric W. Weisstein_, Dec 08 2010

%E a(13) from _Eric W. Weisstein_, Sep 16 2011

%E a(14) from _Eric W. Weisstein_, Sep 17 2011

%E a(15) from _Eric W. Weisstein_, Jul 18 2013

%E a(16) from _Syed Fahad_, Apr 27 2021

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)