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%I #31 Mar 06 2024 04:49:37
%S 4,5,2,7,8,2,9,5,6,6,1,6,0,8,7,9,1,4,0,8,8,2,6,9,5,9,8,8,0,7,0,4,6,9,
%T 6,4,6,9,2,9,8,3,3,6,3,2,7,6,9,7,2,8,3,7,4,0,6,5,0,6,1,7,9,2,0,0,9,8,
%U 6,2,9,8,3,4,1,3,1,3,5,4,2,7,3,2,3,0,8,6,1,5,0,7,1,7,0,7,0,9,5,1,5,2,0,4,1
%N Decimal expansion of Freiman's constant.
%C Named after the Russian-Israeli mathematician Gregory Abelevich Freiman (b. 1926). - _Amiram Eldar_, Jun 15 2021
%D John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, pp. 188-189.
%D Thomas W. Cusick and Mary E. Flahive, The Markoff and Lagrange spectra, American Mathematical Society, 1989, p. 55.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.31, pp. 199-203.
%D G. A. Freiman, Diophantine approximations and the geometry of numbers (Markov's problem) (in Russian), Kalininskii Gosudarstvennyi Universitet, Kalinin, 1975.
%D Julian Havil, The Irrationals, Princeton University Press, Princeton and Oxford, 2012, p. 175.
%H Oleg Karpenkov and Matty van Son, <a href="https://doi.org/10.1016/j.jnt.2020.01.010">Generalised Markov numbers</a>, Journal of Number Theory, Vol. 213 (2020), pp. 16-66; <a href="https://arxiv.org/abs/1809.01688">arXiv preprint</a>, arXiv:1809.01688 [math.NT], 2018. See p. 3.
%H Jouni Parkkonen and Frédéric Paulin, <a href="http://dx.doi.org/10.2140/gt.2010.14.277">Prescribing the behaviour of geodesics in negative curvature</a>, Geom. Topol. 14 (2010) 277-392
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FreimansConstant.html">Freiman's Constant.</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Markov_spectrum">Markov spectrum</a>.
%F The constant is (2221564096 + 283748*sqrt(462))/491993569 = 4 + (253589820 + 283748*sqrt(462))/491993569. See the programs and the references. - _Wolfdieter Lang_, May 29 2018
%e 4.52782956616087914088269598807046964692983363276972837406506179200...
%t RealDigits[(2221564096 + 283748Sqrt@462)/491993569, 10, 111][[1]] (* _Robert G. Wilson v_, May 04 2006 *)
%o (PARI) (2221564096 + 283748*sqrt(462))/491993569 \\ _Charles R Greathouse IV_, Oct 31 2014
%K nonn,cons
%O 1,1
%A _Philippe Deléham_, May 04 2006
%E More terms from _Robert G. Wilson v_, May 04 2006
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