This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A143347 #33 Feb 16 2025 08:33:08
%S A143347 8,5,0,7,3,6,1,8,8,2,0,1,8,6,7,2,6,0,3,6,7,7,9,7,7,6,0,5,3,2,0,6,6,6,
%T A143347 0,4,4,1,1,3,9,9,4,9,3,0,8,2,7,1,0,6,4,7,7,2,8,1,6,8,2,6,1,0,3,1,8,3,
%U A143347 0,1,5,8,4,5,9,3,1,9,4,4,5,3,4,8,5,4,5,9,8,2,6,4,2,1,9,3,9,2,3,9,9,6,0,9,1
%N A143347 Decimal expansion of the paper-folding constant, or the dragon constant.
%C A143347 Named "the Gaussian Liouville number" by Borwein and Coons (2008). - _Amiram Eldar_, Apr 29 2021
%D A143347 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.
%D A143347 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 6.8.5 Paper Folding, pages 439-440.
%H A143347 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, p. 744.
%H A143347 Peter Borwein and Michael Coons, <a href="https://arxiv.org/abs/0806.1694">Transcendence of the Gaussian Liouville number and relatives</a>, arXiv:0806.1694 [math.NT], 2008.
%H A143347 Michael J. Coons, <a href="https://summit.sfu.ca/item/9417">Some aspects of analytic number theory: parity, transcendence, and multiplicative functions</a>, Ph.D. Thesis, Department of Mathematics, Simon Fraser University, 2009.
%H A143347 Chandler Davis and Donald E. Knuth, <a href="/A005811/a005811.pdf">Number Representations and Dragon Curves</a>, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. [Cached copy, with permission]
%H A143347 J. H. Loxton, <a href="https://doi.org/10.1017/S0004972700021341">A method of Mahler in transcendence theory and some of its applications</a>, Bulletin of the Australian Mathematical Society, Vol. 29, No. 1 (1984), pp. 127-136.
%H A143347 Michel Mendès France and Alf van der Poorten, <a href="https://doi.org/10.1017/S0004972700007486">Arithmetic and Analytic Properties of Paper Folding Sequences</a>, Bulletin of the Australian Mathematical Society, volume 24, issue 1, 1981, pages 123-131.
%H A143347 A. J. van der Poorten and J. H. Loxton, <a href="https://doi.org/10.1515/crll.1982.330.159">Arithmetic properties of the solutions of a class of functional equations</a>, Journal für die reine und angewandte Mathematik, Vol. 330 (1982), pp. 159-172; <a href="https://eudml.org/doc/urn:eudml:doc:152410">alternative link</a>.
%H A143347 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PaperFoldingConstant.html">Paper Folding Constant</a>.
%H A143347 <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%H A143347 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A143347 Equals Sum_{k>=1} A014577(k)/2^k = Sum_{k>=1} (1+A034947(k))/2^(k+1). - _Amiram Eldar_, Apr 29 2021
%e A143347 0.85073618820186726036...
%t A143347 RealDigits[ N[ Sum[ 8^2^k/(2^2^(k + 2) - 1), {k, 0, Infinity}], 110]][[1]][[1 ;; 105]] (* _Jean-François Alcover_, Oct 26 2012 *)
%o A143347 (PARI) default(realprecision,510);
%o A143347 c=sum(k=0, 10, 1.0/( 2^(2^k) * ( 1 - 1/(2^(2^(k+2))) ) ) )
%o A143347 /* _Joerg Arndt_, Aug 28 2011 */
%Y A143347 Cf. A014577 (binary expansion), A034947.
%K A143347 nonn,cons
%O A143347 0,1
%A A143347 _Eric W. Weisstein_, Aug 09 2008