cp's OEIS Frontend

A014967 Continued fraction for Conway's constant.

%I A014967 #17 Feb 16 2025 08:32:33
%S A014967 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,
%T A014967 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,
%U A014967 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
%N A014967 Continued fraction for Conway's constant.
%D A014967 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.
%H A014967 Harry J. Smith, <a href="/A014967/b014967.txt">Table of n, a(n) for n = 0..20000</a>
%H A014967 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A014967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConwaysConstant.html">Conways Constant</a>
%H A014967 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A014967 1.303577269034296391257099112... = 1 + 1/(3 + 1/(3 + 1/(2 + 1/(2 + ...)))) [From _Harry J. Smith_, May 12 2009]
%t A014967 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]
%o A014967 Contribution from _Harry J. Smith_, May 15 2009: (Start)
%o A014967 (PARI) { allocatemem(932245000); default(realprecision, 21000); x=NULL; r=solve(x=1, 2,\
%o A014967 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 A014967 -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 A014967 +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 A014967 +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 A014967 +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 A014967 -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 A014967 +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 A014967 -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)
%Y A014967 Cf. A005150, A014715, A014715 (decimal expansion).
%K A014967 cofr,nonn
%O A014967 0,2
%A A014967 _Eric W. Weisstein_
%E A014967 More terms from _Hans Havermann_, Feb 15 2001
%E A014967 Deleted old PARI program _Harry J. Smith_, May 19 2009