

A033089


Incrementally largest terms in the continued fraction for Pi.


5



3, 7, 15, 292, 436, 20776, 78629, 179136, 528210, 12996958, 878783625, 5408240597, 5916686112, 9448623833, 9787547328, 52662113289
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OFFSET

1,1


COMMENTS

There is no larger term in the first 15000000000 terms of the c.f.  Eric W. Weisstein, Jul 27 2013
There is no larger term in the first 30000000000 terms of the c.f.  Syed Fahad, Apr 27 2021


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.
Eric Weisstein's World of Mathematics, Pi
Eric Weisstein's World of Mathematics, Pi Continued Fraction
Index entries for sequences related to the number Pi


MATHEMATICA

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


CROSSREFS

Apart from initial term, same as A007541.
Cf. A033090 (indices), A000796, A001203.
Sequence in context: A077775 A197594 A206851 * A175878 A180503 A153578
Adjacent sequences: A033086 A033087 A033088 * A033090 A033091 A033092


KEYWORD

nonn,hard,changed


AUTHOR

Eric W. Weisstein, Bill Gosper


EXTENSIONS

Checked by Hans Havermann, Aug 07 2010
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



