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

1,1

Comments

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

Links

Table of n, a(n) for n=1..100.

Formula

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

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

Example

2.2228702297210446706953870215765517723981138799367533...

Mathematica

RealDigits[(1 + Sqrt[4E + 1])/2, 10, 100][[1]] (* Alonso del Arte, Mar 23 2012 *)

Prog

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

Crossrefs

Cf. Continued fraction in A100944.

Sequence in context: A294873 A058788 A013598 * A152660 A339163 A058787

Adjacent sequences: A100940 A100941 A100942 * A100944 A100945 A100946

Keyword

cons,nonn

Author

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

Status

approved