Search: id:A060006
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%I A060006
%S A060006 1,3,2,4,7,1,7,9,5,7,2,4,4,7,4,6,0,2,5,9,6,0,9,0,8,8,5,4,4,7,8,0,9,7,3,
%T A060006 4,0,7,3,4,4,0,4,0,5,6,9,0,1,7,3,3,3,6,4,5,3,4,0,1,5,0,5,0,3,0,2,8,2,7,
%U A060006 8,5,1,2,4,5,5,4,7,5,9,4,0,5,4,6,9,9,3,4,7,9,8,1,7,8,7,2,8,0,3,2,9,9,1
%N A060006 Decimal expansion of real root of x^3-x-1.
%C A060006 Has been also called the silver number, also the plastic number.
%C A060006 This is the smallest Pisot-Vijayaraghavan number, v_3. In general v_n 
               is the smallest positive real solution to the equation (v_n)^n = 
               v_n + 1.
%D A060006 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.2.
%D A060006 M. J. Gazale, Gnomon. Princeton University Press, Princeton, NJ, 1999, 
               see Chap. VII.
%D A060006 Ian Stewart, Tales of a neglected number, Scientific American, No. 6, 
               1966, pp. 92-93.
%H A060006 Harry J. Smith, <a href="b060006.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A060006 S. Plouffe, <a href="http://pi.lacim.uqam.ca/piDATA/pisotv.txt">Smallest 
               Pisot-Vijayaraghavan number to 50000 digits</a>
%H A060006 S. Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/
               math/MiscellaneousMathematicalConstants/chap76.html">The Smallest 
               Pisot-Vijayaraghavan number</a>
%H A060006 F. Rothelius, <a href="http://w1.875.telia.com/~u87509703/mathez/v2v3v4.gif">
               Formulae</a>
%H A060006 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Pisot-VijayaraghavanConstant.html">Link to a section of The World 
               of Mathematics</a>
%H A060006 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PisotNumber.html">Pisot Number</a>
%H A060006 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PlasticConstant.html">Plastic Constant</a>
%H A060006 Wikipedia, <a href="http://en.wikipedia.org/wiki/Plastic_number">Plastic 
               number</a>
%F A060006 Another formula: ((1/2)+((1/6)*sqrt(23/3)))^(1/3) + ((1/2)-((1/6)*sqrt(23/
               3)))^(1/3) [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Oct 17 
               2008]
%F A060006 (1/2+sqrt(23/108))^(1/3) + (1/2-sqrt(23/108))^(1/3) - Henry Bottomley 
               (se16(AT)btinternet.com), May 22 2003
%F A060006 CubeRoot(1 + CubeRoot(1 + CubeRoot(1 + CubeRoot(1 + ...)))) - Gerald 
               McGarvey (Gerald.McGarvey(AT)comcast.net), Nov 26 2004
%F A060006 sqrt(1+1/sqrt(1+1/sqrt(1+1/sqrt(1+...)))) - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), 
               Mar 18 2006
%e A060006 1.32471795724474602596090885447809734...
%t A060006 RealDigits[ Solve[x^3 - x - 1 == 0, x][[1, 1, 2]], 10, 111][[1]] [From 
               Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009]
%o A060006 (PARI) { allocatemem(932245000); default(realprecision, 20080); x=solve(x=1, 
               2, x^3 - x - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b060006.txt", 
               n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jul 01 2009]
%Y A060006 v_2 = A001622. A072117 gives continued fraction.
%Y A060006 Cf. A006888, A051016, A051017, A084252.
%Y A060006 Sequence in context: A039915 A085346 A121861 this_sequence A123097 A134571 
               A054086
%Y A060006 Adjacent sequences: A060003 A060004 A060005 this_sequence A060007 A060008 
               A060009
%K A060006 cons,nice,nonn
%O A060006 1,2
%A A060006 Fabian Rothelius (fabian.rothelius(AT)telia.com), Mar 14 2001
%E A060006 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 03 
               2002

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