A033089 Incrementally largest terms in the continued fraction for Pi.

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

Offset: 1

Author

Eric W. Weisstein, Bill Gosper

Keywords

• nonn
• hard

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

• Syed Fahad, 30 billion terms of the simple continued fraction of Pi
• 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
• Index entries for sequences related to the number Pi

Crossrefs

Apart from initial term, same as A007541.

Cf. A033090 (indices), A000796, A001203.

Programs

Mathematica

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

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