A118472 Decimal expansion of Freiman's constant.

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, 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, 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

Offset

1,1

Comments

Named after the Russian-Israeli mathematician Gregory Abelevich Freiman (b. 1926). - Amiram Eldar, Jun 15 2021

References

John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, pp. 188-189.

Thomas W. Cusick and Mary E. Flahive, The Markoff and Lagrange spectra, American Mathematical Society, 1989, p. 55.

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.31, pp. 199-203.

G. A. Freiman, Diophantine approximations and the geometry of numbers (Markov's problem) (in Russian), Kalininskii Gosudarstvennyi Universitet, Kalinin, 1975.

Julian Havil, The Irrationals, Princeton University Press, Princeton and Oxford, 2012, p. 175.

Links

Table of n, a(n) for n=1..105.

Oleg Karpenkov and Matty van Son, Generalised Markov numbers, Journal of Number Theory, Vol. 213 (2020), pp. 16-66; arXiv preprint, arXiv:1809.01688 [math.NT], 2018. See p. 3.

Jouni Parkkonen and Frédéric Paulin, Prescribing the behaviour of geodesics in negative curvature, Geom. Topol. 14 (2010) 277-392

Eric Weisstein's World of Mathematics, Freiman's Constant..

Wikipedia, Markov spectrum.

Formula

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

Example

4.52782956616087914088269598807046964692983363276972837406506179200...

Mathematica

RealDigits[(2221564096 + 283748Sqrt@462)/491993569, 10, 111][[1]] (* Robert G. Wilson v, May 04 2006 *)

Prog

(PARI) (2221564096 + 283748*sqrt(462))/491993569 \\ Charles R Greathouse IV, Oct 31 2014

Crossrefs

Sequence in context: A090201 A130144 A354634 * A356151 A194880 A111624

Adjacent sequences: A118469 A118470 A118471 * A118473 A118474 A118475

Keyword

nonn,cons

Author

Philippe Deléham, May 04 2006

Extensions

More terms from Robert G. Wilson v, May 04 2006

Status

approved