A271529 - OEIS

%I #6 Apr 20 2016 11:26:41

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

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

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

%N Decimal expansion of sqrt(e + e*sqrt(e + e*sqrt(e + ...))).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/e.html">e</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NestedRadical.html">Nested Radical</a>

%F Equals sqrt(e)*(sqrt(e) + sqrt(e + 4))/2.

%F Equals e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/...))))))))).

%e 3.495854711908497636885040848013394528609516258957759538...

%t RealDigits[Sqrt[E] ((Sqrt[E] + Sqrt[E + 4])/2), 10, 120][[1]]

%o (PARI) exp(1)/2+sqrt(4*exp(1)+exp(2))/2 \\ _Charles R Greathouse IV_, Apr 20 2016

%o (PARI) t=exp(.5); t*(t+sqrt(exp(1)+4))/2 \\ _Charles R Greathouse IV_, Apr 20 2016

%Y Cf. A001113, A019774, A100943, A189970, A268580.

%K nonn,cons

%O 1,1

%A _Ilya Gutkovskiy_, Apr 09 2016