OFFSET
0,1
COMMENTS
Named "the Gaussian Liouville number" by Borwein and Coons (2008). - Amiram Eldar, Apr 29 2021
REFERENCES
Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves -- I and II, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. Reprinted in Donald E. Knuth, Selected Papers on Fun and Games, CSLI Publications, 2010, pages 571-614.
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 6.8.5 Paper Folding, pages 439-440.
LINKS
Joerg Arndt, Matters Computational (The Fxtbook), p. 744.
Peter Borwein and Michael Coons, Transcendence of the Gaussian Liouville number and relatives, arXiv:0806.1694 [math.NT], 2008.
Michael J. Coons, Some aspects of analytic number theory: parity, transcendence, and multiplicative functions, Ph.D. Thesis, Department of Mathematics, Simon Fraser University, 2009.
J. H. Loxton, A method of Mahler in transcendence theory and some of its applications, Bulletin of the Australian Mathematical Society, Vol. 29, No. 1 (1984), pp. 127-136.
Michel Mendès France and Alf van der Poorten, Arithmetic and Analytic Properties of Paper Folding Sequences, Bulletin of the Australian Mathematical Society, volume 24, issue 1, 1981, pages 123-131.
A. J. van der Poorten and J. H. Loxton, Arithmetic properties of the solutions of a class of functional equations, Journal für die reine und angewandte Mathematik, Vol. 330 (1982), pp. 159-172; alternative link.
Eric Weisstein's World of Mathematics, Paper Folding Constant.
FORMULA
EXAMPLE
0.85073618820186726036...
MATHEMATICA
RealDigits[ N[ Sum[ 8^2^k/(2^2^(k + 2) - 1), {k, 0, Infinity}], 110]][[1]][[1 ;; 105]] (* Jean-François Alcover, Oct 26 2012 *)
PROG
(PARI) default(realprecision, 510);
c=sum(k=0, 10, 1.0/( 2^(2^k) * ( 1 - 1/(2^(2^(k+2))) ) ) )
/* Joerg Arndt, Aug 28 2011 */
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Aug 09 2008
STATUS
approved