

A033090


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


4



1, 2, 3, 5, 308, 432, 28422, 156382, 267314, 453294, 11504931, 849955263, 2349980289, 3588031780, 8600404591, 15621034283
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..16.
Syed Fahad, 30 billion terms of the simple continued fraction of Pi
E. Fontich, C. SimÃ³, and A. Vieiro, On the "hidden" harmonics associated to best approximants due to quasiperiodicity in splitting phenomena, Regular and Chaotic Dynamics (2018), Pleiades Publishing, Vol. 23, Issue 6, 638653. Also PDF.
Eric Weisstein's World of Mathematics, Pi
Eric Weisstein's World of Mathematics, Pi Continued Fraction


MATHEMATICA

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


CROSSREFS

Cf. A033089, A001203.
Sequence in context: A333803 A338262 A042579 * A303371 A046474 A056146
Adjacent sequences: A033087 A033088 A033089 * A033091 A033092 A033093


KEYWORD

nonn,hard


AUTHOR

Eric W. Weisstein, Bill Gosper


EXTENSIONS

a(12) from Eric W. Weisstein, Dec 08 2010
a(13) from Eric W. Weisstein, Sep 16 2011
a(14) from Eric W. Weisstein, Sep 17 2011
a(15) from Eric W. Weisstein, Jul 18 2013
a(16) from Syed Fahad, Apr 27 2021


STATUS

approved



