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A033090 Indices of incrementally largest terms in the continued fraction for Pi. 4


%S 1,2,3,5,308,432,28422,156382,267314,453294,11504931,849955263,

%T 2349980289,3588031780,8600404591,15621034283

%N Indices of incrementally largest terms in the continued fraction for Pi.

%C This sequence assumes nonstandard indexing of continued fraction terms as [a_1; a_2, a_3, ...]. If you use the actual offset from A001203, corresponding to [a_0; a_1, a_2, ...], you get instead 0, 1, 2, 4, 307, 431, 28421, ... Compare with A033092 versus A224849. - _Jeppe Stig Nielsen_, Dec 14 2019

%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. Also <a href="http://www.maia.ub.es/~carles/moser90.pdf">PDF</a>.

%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>

%t With[{s = ContinuedFraction[Pi, 2*10^7]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Jan 31 2020 *)

%Y Cf. A033089, A001203.

%K nonn,hard,changed

%O 1,2

%A _Eric W. Weisstein_, _Bill Gosper_

%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 12 02:06 EDT 2021. Contains 343808 sequences. (Running on oeis4.)