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A199879 Continued fraction for x value of the unique pairwise intersection on (0,1) of distinct order 5 power tower functions with parentheses inserted. 2
0, 2, 2, 1, 35, 1, 2, 2, 1, 2, 5, 3, 1, 1, 45, 1, 1, 6, 11, 2, 9, 2, 2, 2, 2, 1, 1, 1, 29, 1, 3, 7, 4, 1, 7, 61, 1, 1, 2, 1, 2, 6, 2, 1, 1, 96, 11, 1, 2, 1, 1, 4, 14, 1, 10, 1, 2, 1, 7, 4, 7, 5, 10, 1, 6, 2, 2, 9, 6, 8, 3, 1, 3, 1, 3, 7, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..77.

EXAMPLE

0.42801103796472992390204...

MAPLE

with(numtheory):

f:= x-> (x^(x^x))^(x^x): g:= x-> x^(x^((x^x)^x)):

Digits:= 200:

xv:= fsolve(f(x)=g(x), x=0..0.99):

cfrac(evalf(xv), 120, 'quotients')[];

MATHEMATICA

terms = 77; digits = terms+10; xv = x /. FindRoot[x^(x^2) - 2x == 0, {x, 1/2}, WorkingPrecision -> digits]; ContinuedFraction[xv, terms] (* Jean-Fran├žois Alcover, Mar 24 2017 *)

CROSSREFS

Cf. A199814 (decimal expansion), A199880 (Engel expansion).

Sequence in context: A048660 A019227 A163893 * A006828 A091752 A078078

Adjacent sequences:  A199876 A199877 A199878 * A199880 A199881 A199882

KEYWORD

nonn,cofr

AUTHOR

Alois P. Heinz, Nov 11 2011

STATUS

approved

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Last modified September 25 23:58 EDT 2021. Contains 347664 sequences. (Running on oeis4.)