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

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, 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, 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

Offset

0,1

Comments

Feigenbaum bifurcation velocity delta. See A006890 for further information.

Apart from the first term, the same as A069544. - R. J. Mathar, Apr 28 2009

Links

Harry J. Smith, Table of n, a(n) for n = 0..964 [shortened by Kevin Ryde, Sep 30 2024]

Example

4.66920160910299067185320382... = 4 + 1/(1 + 1/(2 + 1/(43 + 1/(2 + ...))))

Mathematica

fbvd = (* copy value from the link in A006890 or immediately above *); ContinuedFraction@ fbvd (* Robert G. Wilson v, Apr 27 2009 *)

Prog

(PARI) { default(realprecision, 1019); delta=4.\
6692016091029906718532038204662016172581855774757686327456513430\
0413433021131473713868974402394801381716598485518981513440862714\
2027932522312442988890890859944935463236713411532481714219947455\
6443658237932020095610583305754586176522220703854106467494942849\
8145339172620056875566595233987560382563722564800409510712838906\
1184470277585428541980111344017500242858538249833571552205223608\
7250291678860362674527213399057131606875345083433934446103706309\
4520191158769724322735898389037949462572512890979489867683346116\
2688911656312347446057517953912204556247280709520219819909455858\
1946136877445617396074115614074243754435499204869180982648652368\
4387027996490173977934251347238087371362116018601281861020563818\
1835409759847796417390032893617143215987824078977661439139576403\
7760537119096932066998361984288981837003229412030210655743295550\
3888458497370347275321219257069584140746618419819610061296401614\
8771294441590140546794180019813325337859249336588307045999993837\
5411726563553016862529032210862320550634510679399023341675; A159766=contfrac(delta); for (n=1, 967, write("b159766.txt", n-1, " ", A159766[n])); } \\ Harry J. Smith, May 15 2009
(PARI) A159766=contfrac(delta) \\ M. F. Hasler, Apr 30 2018

Crossrefs

Cf. A006890 (decimal expansion of the constant), A069544 (continued fraction of the fractional part), A069261 (Egyptian fraction).

Sequence in context: A299728 A299839 A265178 * A280284 A004161 A303141

Adjacent sequences: A159763 A159764 A159765 * A159767 A159768 A159769

Keyword

nonn,cofr

Author

Harry J. Smith, Apr 21 2009

Extensions

Old PARI program deleted by Harry J. Smith, May 19 2009

Status

approved