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 A002211 Continued fraction for Khintchine's constant. (Formerly M0118 N0047) 14

%I M0118 N0047

%S 2,1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,3,1,1,1,90,2,1,12,1,1,1,1,5,

%T 2,6,1,6,3,1,1,2,5,2,1,2,1,1,4,1,2,2,3,2,1,1,4,1,1,2,5,2,1,1,3,29,8,3,

%U 1,4,3,1,10,50,1,2,2,7,6,2,2,16,4,4,2,2,3,1,1,7,1,5,1,2,1,5,3,1

%N Continued fraction for Khintchine's constant.

%C Incrementally larger terms in the continued fraction for Khintchine's constant: 1, 2, 5, 10, 24, 90, 770, 941, 11759, 54097, 231973, ..., and they occur at 1, 2, 3, 10, 15, 23, 104, 1701, 2445, 18995, 60037, ... - _Robert G. Wilson v_, Dec 09 2013

%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).

%H T. D. Noe, <a href="/A002211/b002211.txt">Table of n, a(n) for n = 0..999</a>

%H H. Havermann, <a href="http://chesswanks.com/pxp/cfk.html">Simple Continued Fraction Expansion of Khinchin's Constant</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 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.

%H J. W. Wrench, Jr. and D. Shanks, <a href="http://www.jstor.org/stable/2003606">Questions concerning Khintchine's constant and the efficient computation of regular continued fractions</a>, Math. Comp., 20 (1966), 444-448.

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

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%e 2.685452001065306445309714835... = 2 + 1/(1 + 1/(2 + 1/(5 + 1/(1 + ...))))

%e [a_0; a_1, a_2, ...] = [2, 1, 2, ...]

%t ContinuedFraction[Khinchin, 100]

%Y Cf. A002210.

%K cofr,nonn,nice,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Robert G. Wilson v_, Oct 31 2001

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)