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A159767 Continued fraction expansion of A006891. 2

%I #11 Aug 01 2015 12:15:47

%S 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 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 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 Continued fraction expansion of A006891.

%C Feigenbaum bifurcation velocity alpha.

%H Harry J. Smith, <a href="/A159767/b159767.txt">Table of n, a(n) for n = 0..995</a>

%e -alpha = 2.50290787509589282... = 2 + 1/(1 + 1/(1 + 1/(85 + 1/(2 + ...))))

%t (* assign to 'x' the Feigenbaum bifurcation velocity alpha *); ContinuedFraction[ x, 100] (* _Robert G. Wilson v_, May 31 2009 *)

%o From _Harry J. Smith_, May 15 2009: (Start)

%o (PARI) { default(realprecision,1019); alpha=-2.\

%o 5029078750958928222839028732182157863812713767271499773361920567\

%o 7923546317959020670329964974643383412959523186999585472394218237\

%o 7785445179272863314993372578112163594879503744781260997380598671\

%o 2397117373289276654044010306698313834600094139322364490657889951\

%o 2205843172507873377463087853424285351988587500042358246918740820\

%o 4281700901714823051821621619413199856066129382742649709844084470\

%o 1008054549677936760888126446406885181552709324007542506497157047\

%o 0475419932831783645332562415378693957125097066387979492654623137\

%o 6745918909813116752434221110130913127837160951158341230841503716\

%o 4997020224681219644081216686527458043026245782561067150138521821\

%o 6449532543349873487413352795815351016583605455763513276501810781\

%o 1948369459574850237398235452625632779475397269902012891516645793\

%o 9420198920248803394051699686551494477396533876979741232354061781\

%o 9896112494095990353128997733611849847377946108428833293833903950\

%o 9008914086351525626803381414669279913310743349705143545201344643\

%o 4264752001621384610729922641994332772918977769053802596851; x=contfrac(-alpha); for (n=1, 996, write("b159767.txt", n-1, " ", x[n])); } (End)

%K nonn,cofr

%O 0,1

%A _Harry J. Smith_, Apr 21 2009

%E Old PARI program deleted by _Harry J. Smith_, May 19 2009

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)