OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, e
Eric Weisstein's World of Mathematics, Nested Radical
FORMULA
Equals sqrt(e)*(sqrt(e) + sqrt(e + 4))/2.
Equals e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/...))))))))).
EXAMPLE
3.495854711908497636885040848013394528609516258957759538...
MATHEMATICA
RealDigits[Sqrt[E] ((Sqrt[E] + Sqrt[E + 4])/2), 10, 120][[1]]
PROG
(PARI) exp(1)/2+sqrt(4*exp(1)+exp(2))/2 \\ Charles R Greathouse IV, Apr 20 2016
(PARI) t=exp(.5); t*(t+sqrt(exp(1)+4))/2 \\ Charles R Greathouse IV, Apr 20 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Apr 09 2016
STATUS
approved