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First position of n in continued fraction for Khinchin's constant.
3

%I #22 Aug 14 2024 18:55:21

%S 2,1,10,47,4,34,76,65,119,11,104,27,103,110,675,80,1080,146,142,369,

%T 246,586,679,16,1428,1621,1021,1627,64,1342,799,157,409,506,1406,1783,

%U 1445,206,3160,300,2683,2037,4207,5204,271,523,368,7892,2255,72,970

%N First position of n in continued fraction for Khinchin's constant.

%C Indexing of the terms is based on writing a c.f. as [a_1; a_2, a_3, ...]; the more standard convention of [a_0; a_1, a_2, ...] requires subtracting 1 from each term of the sequence.

%C Smallest positive integers not occurring in the first 106621 terms of the c.f. are 236, 260, 265, 279, 282, 290, 294, 297, 299, ... - _Eric W. Weisstein_, Oct 01 2011

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

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

%F a(n) = A224851(n) + 1.

%Y Cf. A224851 (= a(n) - 1).

%Y Cf. A002211, A054866, A054870.

%K nonn

%O 1,1

%A _Hans Havermann_, May 27 2000