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A014715 Decimal expansion of Conway's constant. 6

%I

%S 1,3,0,3,5,7,7,2,6,9,0,3,4,2,9,6,3,9,1,2,5,7,0,9,9,1,1,2,1,5,2,5,5,1,

%T 8,9,0,7,3,0,7,0,2,5,0,4,6,5,9,4,0,4,8,7,5,7,5,4,8,6,1,3,9,0,6,2,8,5,

%U 5,0,8,8,7,8,5,2,4,6,1,5,5,7,1,2,6,8,1,5,7,6,6,8,6,4,4,2,5,2,2,5,5,5

%N Decimal expansion of Conway's constant.

%C An algebraic integer of degree 71. - _Charles R Greathouse IV_, Aug 10 2014

%D J. H. Conway, The weird and wonderful chemistry of audioactive decay, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.

%D Clifford A. Pickover, The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publ., NY, 2009, page 486.

%D I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.

%H Harry J. Smith, <a href="/A014715/b014715.txt">Table of n, a(n) for n = 1..20000</a>

%H Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, <a href="https://arxiv.org/abs/2006.06837">Stuttering Conway Sequences Are Still Conway Sequences</a>, arXiv:2006.06837 [math.DS], 2020.

%H John Conway and Brady Haran, <a href="https://www.youtube.com/watch?v=ea7lJkEhytA">Look-and-Say Numbers</a> (2014).

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/cnwy/cnwy.html">Conway's Constant</a>

%H S. R. Finch, <a href="http://web.archive.org/web/20010207194413 /http://www.mathsoft.com/asolve/constant/cnwy/cnwy.html">Conway's Constant</a> [From the Wayback Machine]

%H Thomas Morrill, <a href="https://arxiv.org/abs/2004.06414">Look, Knave</a>, arXiv:2004.06414 [math.CO], 2020.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConwaysConstant.html">Conways Constant</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LookandSaySequence.html">Lookand Say Sequence</a>

%e 1.303577269034296391257099112152551890730702504659404875754861390628550...

%t RealDigits[ NSolve[{0 == Plus @@ ({1, 0, -1, -2, -1, 2, 2, 1, -1, -1, -1, -1, -1, 2, 5, 3, -2, -10, -3, -2, 6, 6, 1, 9, -3, -7, -8, -8, 10, 6, 8, -5, -12, 7, -7, 7, 1, -3, 10, 1, -6, -2, -10, -3, 2, 9, -3, 14, -8, 0, -7, 9, 3, -4, -10, -7, 12, 7, 2, -12, -4, -2, 5, 0, 1, -7, 7, -4, 12, -6, 3, -6} x^Range[71, 0, -1])}, {x}, 105][[-1, -1, -1]]][[1]] (* _Ryan Propper_, Jul 29 2005 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 20080); x=NULL; r=solve(x=1, 2,\

%o x^71-x^69-2*x^68-x^67+2*x^66+2*x^65+x^64-x^63-x^62-x^61-x^60\

%o -x^59+2*x^58+5*x^57+3*x^56-2*x^55-10*x^54-3*x^53-2*x^52+6*x^51\

%o +6*x^50+x^49+9*x^48-3*x^47-7*x^46-8*x^45-8*x^44+10*x^43+6*x^42\

%o +8*x^41-5*x^40-12*x^39+7*x^38-7*x^37+7*x^36+x^35-3*x^34+10*x^33\

%o +x^32-6*x^31-2*x^30-10*x^29-3*x^28+2*x^27+9*x^26-3*x^25+14*x^24\

%o -8*x^23-7*x^21+9*x^20+3*x^19-4*x^18-10*x^17-7*x^16+12*x^15\

%o +7*x^14+2*x^13-12*x^12-4*x^11-2*x^10+5*x^9+x^7-7*x^6+7*x^5\

%o -4*x^4+12*x^3-6*x^2+3*x-6); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b014715.txt", n, " ", d)); } \\ _Harry J. Smith_, May 15 2009

%o (PARI) P=Pol([1, 0, -1, -2, -1, 2, 2, 1, -1, -1, -1, -1, -1, 2, 5, 3, -2, -10, -3, -2, 6, 6, 1, 9, -3, -7, -8, -8, 10, 6, 8, -5, -12, 7, -7, 7, 1, -3, 10, 1, -6, -2, -10, -3, 2, 9, -3, 14, -8, 0, -7, 9, 3, -4, -10, -7, 12, 7, 2, -12, -4, -2, 5, 0, 1, -7, 7, -4, 12, -6, 3, -6]); polrootsreal(P)[3] \\ _Charles R Greathouse IV_, Aug 10 2014

%Y Cf. A014967, A005150, A006715, A006751, A014967 (continued fraction).

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_

%E More terms from _Eric W. Weisstein_, Jul 01 2003

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