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A072551 Decimal expansion of sqrt(e^(1/e)) = 1.20194336847031... 0

%I

%S 1,2,0,1,9,4,3,3,6,8,4,7,0,3,1,4,4,6,7,1,9,4,2,4,1,1,3,9,3,8,1,2,9,7,

%T 0,8,0,4,4,0,1,8,7,1,5,3,9,3,5,1,6,9,0,9,5,6,3,0,9,8,9,0,1,3,8,3,1,5,

%U 7,8,4,5,1,1,2,1,6,8,1,0,7,1,8,4,9,4,4,4,1,8,1,4,3,0,2,1,6,3,8,2,4,2,1,9,6

%N Decimal expansion of sqrt(e^(1/e)) = 1.20194336847031...

%C This constant is related to the convergence properties of the following simple algorithm: w(n+2) = A^( w(n+1) + w(n) ) where A is a positive real. Take any w(1), w(2) reals>0, then w(n) converges if and only if, 0 < A < sqrt(e^(1/e)). For example if A=1/2 w(n) converges to 1/2, if A=1/3, w(n) converges to 0.408004405...(If w(n) converges the limit L is always independent of initial values w(1),w(2) and L is < e).

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.

%t RealDigits[E^(E^-1/2), 10, 110] [[1]]

%Y See also A073229 for e^(1/e).

%K cons,nonn

%O 1,2

%A _Benoit Cloitre_, Aug 05 2002

%E Edited by _Robert G. Wilson v_, Aug 08 2002

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Last modified April 19 17:29 EDT 2021. Contains 343117 sequences. (Running on oeis4.)