A100943 Decimal expansion of the nested surd sqrt(e + sqrt(e + sqrt(e + ...))).
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, 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, 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
Offset: 1
Examples
2.2228702297210446706953870215765517723981138799367533...
Programs
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Mathematica
RealDigits[(1 + Sqrt[4E + 1])/2, 10, 100][[1]] (* Alonso del Arte, Mar 23 2012 *)
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PARI
default(realprecision,100);t=0;for(n=1,5000,t=sqrt(t+exp(1)));return(t)
Formula
Solution of y^2-y-e=0.
Closed form: (1 + sqrt(4e + 1))/2. [Alonso del Arte, Mar 23 2012]