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A100943 Decimal expansion of the nested surd sqrt(e + sqrt(e + sqrt(e + ...))). 3

%I

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

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

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

%N Decimal expansion of the nested surd sqrt(e + sqrt(e + sqrt(e + ...))).

%C e is the natural logarithm base (see A001113 for decimal expansion).

%F Solution of y^2-y-e=0. [Hudson]

%F Closed form: (1 + sqrt(4e + 1))/2 [Alonso del Arte, Mar 23 2012]

%e 2.2228702297210446706953870215765517723981138799367533...

%t RealDigits[(1 + Sqrt[4E + 1])/2, 10, 100][[1]] (* _Alonso del Arte_, Mar 23 2012 *)

%o (PARI) default(realprecision,100):t=0:for(n=1,5000,t=sqrt(t+exp(1))):return(t)

%Y Cf. Continued fraction in A100944.

%K cons,nonn

%O 1,1

%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 23 2004

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)