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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Computed using a developmental version of Mathematica.

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..15.

E. Fontich, C. Simó, 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, 638-653. 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: A082755 A042067 A042579 * A303371 A046474 A056146

Adjacent sequences:  A033087 A033088 A033089 * A033091 A033092 A033093

KEYWORD

nonn,hard,changed

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

STATUS

approved

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Last modified February 18 09:39 EST 2020. Contains 332011 sequences. (Running on oeis4.)