A224849 -id:A224849 - cp's OEIS frontend

A033090 Indices of incrementally largest terms in the continued fraction for Pi.

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

Offset: 1

Eric W. Weisstein, Bill Gosper

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

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. Also PDF.
Eric Weisstein's World of Mathematics, Pi
Eric Weisstein's World of Mathematics, Pi Continued Fraction

Cf. A033089, A001203.

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

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

A033092 Positions of incrementally largest terms in the continued fraction for Euler's constant gamma (A002852).

Original entry on oeis.org

1, 2, 4, 8, 10, 20, 31, 34, 40, 529, 5041, 15347, 25318, 28321, 33261, 158568, 273272, 3233049, 4198630, 11925232, 21988970, 27999430, 130169954, 133517598, 560882701, 1060718271, 1158300012, 1183752952, 3652709607

Offset: 0

Eric W. Weisstein and Bill Gosper

nonn

This sequence assumes nonstandard indexing of c.f. terms as [a_1; a_2, a_3, ...].

No other maximum term occurs in the first 4,851,382,841 terms of the c.f. - Eric W. Weisstein, Jul 22 2013

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Continued Fraction

Cf. A224849 (= a(n) - 1).
Cf. A002852 (continued fraction for Euler's constant).
Cf. A033091 (values of incrementally largest terms in c.f.).
Cf. A001620 (decimal expansion of Euler's constant).
Cf. A098967.

a(n) = A224849(n) + 1.

More terms from Eric W. Weisstein, Oct 25 2004
More terms from Eric W. Weisstein, Jan 02 2007
a(22) and a(23) from Eric W. Weisstein, Dec 09 2010
a(24) from Eric W. Weisstein, Sep 21 2011
a(25)-a(28) from Eric W. Weisstein, Jul 22 2013

cp's OEIS Frontend

A033090 Indices of incrementally largest terms in the continued fraction for Pi.

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