(Translated by https://www.hiragana.jp/)
A033089 - OEIS
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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
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
E. Fontich, C. Simó, 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, 638-653.
Eric Weisstein's World of Mathematics, Pi
Eric Weisstein's World of Mathematics, Pi Continued Fraction
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 * A370661 A175878 A180503
KEYWORD
nonn,hard
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