A014715 Decimal expansion of Conway's constant.

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, 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, 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

Offset

1,2

Comments

An algebraic integer of degree 71. - Charles R Greathouse IV, Aug 10 2014

References

John 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.

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 209.

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

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.

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

Links

Edward Krogius Table of n, a(n) for n = 1..50000 (terms 1..20000 from Harry J. Smith).

Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, and Emanuele Troiani, Stuttering Conway Sequences Are Still Conway Sequences, arXiv:2006.06837 [math.DS], 2020.

Jonathan Comes, Stuttering look and say sequences and a challenger to Conway's most complicated algebraic number from the silliest source, arXiv:2206.11991 [math.HO], 2022.

John H. Conway and Brady Haran, Look-and-Say Numbers (2014).

S. R. Finch, Conway's Constant

S. R. Finch, Conway's Constant [From the Wayback Machine]

Thomas Morrill, Look, Knave, arXiv:2004.06414 [math.CO], 2020.

Eric Weisstein's World of Mathematics, Conways Constant.

Eric Weisstein's World of Mathematics, Lookand Say Sequence.

Index entries for algebraic numbers, degree 71.

Example

1.303577269034296391257099112152551890730702504659404875754861390628550...

Mathematica

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 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 20080); x=NULL; r=solve(x=1, 2, \
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\
-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\
+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\
+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\
+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\
-8*x^23-7*x^21+9*x^20+3*x^19-4*x^18-10*x^17-7*x^16+12*x^15\
+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\
-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
(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

Crossrefs

Cf. A014967, A005150, A006715, A006751.

Sequence in context: A229704 A372865 A380343 * A131656 A194492 A194136

Adjacent sequences: A014712 A014713 A014714 * A014716 A014717 A014718

Keyword

nonn,cons

Author

Eric W. Weisstein

Extensions

More terms from Eric W. Weisstein, Jul 01 2003

Status

approved