A014967 Continued fraction for Conway's constant.

1, 3, 3, 2, 2, 54, 5, 2, 1, 16, 1, 30, 1, 1, 1, 2, 2, 1, 14, 1, 6, 24, 107, 5, 1, 1, 26, 2, 41, 10, 1, 1, 5, 17, 5, 1, 8, 3, 94, 38, 1, 18, 1, 1, 2, 1, 64, 18, 1, 6, 1, 2, 2, 1, 23, 1, 4, 4, 1, 1, 3, 4, 1, 10, 1, 28, 4, 12, 1, 1238, 13, 1, 1, 58, 1, 2, 4, 1, 3, 7, 1, 3, 1, 4, 1, 1, 1, 1, 1, 1, 100

Offset

0,2

References

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.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Eric Weisstein's World of Mathematics, Conways Constant

Index entries for continued fractions for constants

Example

1.303577269034296391257099112... = 1 + 1/(3 + 1/(3 + 1/(2 + 1/(2 + ...)))) [From Harry J. Smith, May 12 2009]

Mathematica

terms = 201; ContinuedFraction[x /. FindRoot[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, {x, 1.3}, WorkingPrecision -> 1.3*terms], terms]

Prog

Contribution from Harry J. Smith, May 15 2009: (Start)
(PARI) { allocatemem(932245000); default(realprecision, 21000); 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); c=contfrac(r); for (n=1, 20001, write("b014967.txt", n-1, " ", c[n])); } (End)

Crossrefs

Cf. A005150, A014715, A014715 (decimal expansion).

Sequence in context: A309569 A356528 A292600 * A210851 A120992 A228483

Adjacent sequences: A014964 A014965 A014966 * A014968 A014969 A014970

Keyword

cofr,nonn

Author

Eric W. Weisstein

Extensions

More terms from Hans Havermann, Feb 15 2001

Deleted old PARI program Harry J. Smith, May 19 2009

Status

approved