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A159766 Continued fraction expansion of the Feigenbaum constant A006890 = 4.66920160910...

%I A159766 #22 Sep 30 2024 12:46:01
%S A159766 4,1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,2,1,1,1,33,1,1,53,1,1,1,1,1,
%T A159766 1,6,1,1,2,2,1,1,239,1,3,31,1,1,11,1,13,123,2,2,2,2,13,15,1,2,3,3,1,3,
%U A159766 1,1,6,1,3,1,1,13,8,1,7,1,2,1,8,7,1,17,1,6,1,1,3,1,1,13,1,1,4,2,9,124,1,1,3
%N A159766 Continued fraction expansion of the Feigenbaum constant A006890 = 4.66920160910...
%C A159766 Feigenbaum bifurcation velocity delta. See A006890 for further information.
%C A159766 Apart from the first term, the same as A069544. - _R. J. Mathar_, Apr 28 2009
%H A159766 Harry J. Smith, <a href="/A159766/b159766.txt">Table of n, a(n) for n = 0..964</a> [shortened by _Kevin Ryde_, Sep 30 2024]
%e A159766 4.66920160910299067185320382... = 4 + 1/(1 + 1/(2 + 1/(43 + 1/(2 + ...))))
%t A159766 fbvd = (* copy value from the link in A006890 or immediately above *); ContinuedFraction@ fbvd (* _Robert G. Wilson v_, Apr 27 2009 *)
%o A159766 (PARI) { default(realprecision,1019); delta=4.\
%o A159766 6692016091029906718532038204662016172581855774757686327456513430\
%o A159766 0413433021131473713868974402394801381716598485518981513440862714\
%o A159766 2027932522312442988890890859944935463236713411532481714219947455\
%o A159766 6443658237932020095610583305754586176522220703854106467494942849\
%o A159766 8145339172620056875566595233987560382563722564800409510712838906\
%o A159766 1184470277585428541980111344017500242858538249833571552205223608\
%o A159766 7250291678860362674527213399057131606875345083433934446103706309\
%o A159766 4520191158769724322735898389037949462572512890979489867683346116\
%o A159766 2688911656312347446057517953912204556247280709520219819909455858\
%o A159766 1946136877445617396074115614074243754435499204869180982648652368\
%o A159766 4387027996490173977934251347238087371362116018601281861020563818\
%o A159766 1835409759847796417390032893617143215987824078977661439139576403\
%o A159766 7760537119096932066998361984288981837003229412030210655743295550\
%o A159766 3888458497370347275321219257069584140746618419819610061296401614\
%o A159766 8771294441590140546794180019813325337859249336588307045999993837\
%o A159766 5411726563553016862529032210862320550634510679399023341675; A159766=contfrac(delta); for (n=1, 967, write("b159766.txt", n-1, " ", A159766[n])); } \\ _Harry J. Smith_, May 15 2009
%o A159766 (PARI) A159766=contfrac(delta) \\ _M. F. Hasler_, Apr 30 2018
%Y A159766 Cf. A006890 (decimal expansion of the constant), A069544 (continued fraction of the fractional part), A069261 (Egyptian fraction).
%K A159766 nonn,cofr
%O A159766 0,1
%A A159766 _Harry J. Smith_, Apr 21 2009
%E A159766 Old PARI program deleted by _Harry J. Smith_, May 19 2009