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A002210 Decimal expansion of Khintchine's constant.
(Formerly M1564 N0609)
45

%I M1564 N0609

%S 2,6,8,5,4,5,2,0,0,1,0,6,5,3,0,6,4,4,5,3,0,9,7,1,4,8,3,5,4,8,1,7,9,5,

%T 6,9,3,8,2,0,3,8,2,2,9,3,9,9,4,4,6,2,9,5,3,0,5,1,1,5,2,3,4,5,5,5,7,2,

%U 1,8,8,5,9,5,3,7,1,5,2,0,0,2,8,0,1,1,4,1,1,7,4,9,3,1,8,4,7,6,9,7,9,9,5,1,5

%N Decimal expansion of Khintchine's constant.

%C _Carles Simó_, Oct 11 2016, reports that he has computed 10^6 terms of this sequence (see links). - _N. J. A. Sloane_, Nov 04 2016

%D S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 59-65

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 164.

%H Harry J. Smith, <a href="/A002210/b002210.txt">Table of n, a(n) for n = 1..1200</a>

%H D. H. Bailey, J. M. Borwein & R. E. Crandall, <a href="http://crd.lbl.gov/~dhbailey/dhbpapers/khinchine.pdf">On the Khintchine Constant</a>

%H D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, <a href="http://crd-legacy.lbl.gov/~dhbailey/dhbpapers/tenproblems.pdf">Ten Problems in Experimental Mathematics</a>

%H Ph. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/publist.html">Zeta function expansions of some classical constants</a>

%H E. Fontich, C. Simó, A. Vieiro, <a href="https://doi.org/10.1134/S1560354718060011">On the "hidden" harmonics associated to best approximants due to quasiperiodicity in splitting phenomena</a>, Regular and Chaotic Dynamics (2018), Pleiades Publishing, Vol. 23, Issue 6, 638-653.

%H Brady Haran and Tony Padilla, <a href="http://www.youtube.com/watch?v=VDD6FDhKCYA">Six Sequences</a>, Numberphile video, 2013.

%H Christian Perfect, <a href="http://aperiodical.com/2013/07/integer-sequence-reviews-on-numberphile-or-vice-versa/">Integer sequence reviews on Numberphile (or vice versa)</a>, 2013.

%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/khintchine.txt">110000 digits of the Khintchine constant</a>

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap50.html">Khinchin constant to 1024 digits</a>

%H D. Shanks and J. W. Wrench, Jr., <a href="http://www.jstor.org/stable/2309633">Khintchine's constant</a>, Amer. Math. Monthly, 66 (1959), 276-279.

%H Carles Simó, <a href="http://www.maia.ub.es/dsg/khinchin">Computation of 10^6 digits of Khintchine's constant</a>

%H Carles Simó, <a href="/A002210/a002210.png">Computation of 10^6 digits of Khintchine's constant</a> [Cached copy, with permission]

%H Carles Simó, <a href="/A002210/a002210.txt">10^6 digits of Khintchine's constant</a> [Cached copy, with permission]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KhinchinsConstant.html">Khinchin's Constant</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KhinchinsConstantDigits.html">Khinchin's Constant Digits</a>

%H Thomas Wieting, <a href="http://dx.doi.org/10.1090/S0002-9939-07-09202-7">A Khinchin Sequence</a>, Proc. Amer. Math. Soc. 136 (2008), 815-824.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Khinchin%27s_constant">Khinchin's constant</a>

%H J. W. Wrench, <a href="http://dx.doi.org/10.1090/S0025-5718-1960-0170455-1">Further evaluation of Khintchine's constant</a>, Math. Comp., 14 (1960), 370-371.

%e 2.685452001065306445309714835481795693820382293994462953051152345557218...

%t RealDigits[N[Khinchin, 100]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 18 2009 *)

%o (Python)

%o from mpmath import *

%o mp.dps=106

%o print map(int, list(str(khinchin).replace('.', ''))[:-1]) # _Indranil Ghosh_, Jul 08 2017

%Y Cf. A002211.

%K nonn,cons,nice

%O 1,1

%A _N. J. A. Sloane_

%E Pari code removed by _D. S. McNeil_, Dec 26 2010

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)