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A159767 Continued fraction expansion of A006891.

%I A159767 #11 Aug 01 2015 12:15:47
%S A159767 2,1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,2,2,1,17,1,1,5,3,2,6,3,5,1,1,
%T A159767 3,3,15,3,1,1,7,2,3,1,7,2,1,55,1,1,1,1,4,9,1,2,1,36,1,5,10,1,1,2,1,4,
%U A159767 1,4,5,5,1,1,130,1,3,1,1,2,1,3,1,3,2,3,2,2,547,9,18,3,1,4,2,1,1,2,2,2,1,6,1
%N A159767 Continued fraction expansion of A006891.
%C A159767 Feigenbaum bifurcation velocity alpha.
%H A159767 Harry J. Smith, <a href="/A159767/b159767.txt">Table of n, a(n) for n = 0..995</a>
%e A159767 -alpha = 2.50290787509589282... = 2 + 1/(1 + 1/(1 + 1/(85 + 1/(2 + ...))))
%t A159767 (* assign to 'x' the Feigenbaum bifurcation velocity alpha *); ContinuedFraction[ x, 100] (* _Robert G. Wilson v_, May 31 2009 *)
%o A159767 From _Harry J. Smith_, May 15 2009: (Start)
%o A159767 (PARI) { default(realprecision,1019); alpha=-2.\
%o A159767 5029078750958928222839028732182157863812713767271499773361920567\
%o A159767 7923546317959020670329964974643383412959523186999585472394218237\
%o A159767 7785445179272863314993372578112163594879503744781260997380598671\
%o A159767 2397117373289276654044010306698313834600094139322364490657889951\
%o A159767 2205843172507873377463087853424285351988587500042358246918740820\
%o A159767 4281700901714823051821621619413199856066129382742649709844084470\
%o A159767 1008054549677936760888126446406885181552709324007542506497157047\
%o A159767 0475419932831783645332562415378693957125097066387979492654623137\
%o A159767 6745918909813116752434221110130913127837160951158341230841503716\
%o A159767 4997020224681219644081216686527458043026245782561067150138521821\
%o A159767 6449532543349873487413352795815351016583605455763513276501810781\
%o A159767 1948369459574850237398235452625632779475397269902012891516645793\
%o A159767 9420198920248803394051699686551494477396533876979741232354061781\
%o A159767 9896112494095990353128997733611849847377946108428833293833903950\
%o A159767 9008914086351525626803381414669279913310743349705143545201344643\
%o A159767 4264752001621384610729922641994332772918977769053802596851; x=contfrac(-alpha); for (n=1, 996, write("b159767.txt", n-1, " ", x[n])); } (End)
%K A159767 nonn,cofr
%O A159767 0,1
%A A159767 _Harry J. Smith_, Apr 21 2009
%E A159767 Old PARI program deleted by _Harry J. Smith_, May 19 2009