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Search: id:A014967
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| A014967 |
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Continued fraction for Conway's constant. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
G. Xiao, Contfrac
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for continued fractions for constants
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EXAMPLE
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1.303577269034296391257099112... = 1 + 1/(3 + 1/(3 + 1/(2 + 1/(2 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 12 2009]
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MATHEMATICA
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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]
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PROGRAM
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Contribution from Harry J. Smith (hjsmithh(AT)sbcglobal.net), 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)
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CROSSREFS
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Cf. A005150, A014715.
Cf. A014715 = Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 12 2009]
Sequence in context: A162235 A113780 A007515 this_sequence A120992 A129979 A075017
Adjacent sequences: A014964 A014965 A014966 this_sequence A014968 A014969 A014970
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KEYWORD
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cofr,nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from Hans Havermann (pxp(AT)rogers.com), Feb 15 2001
Deleted old PARI program Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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