A254689 - OEIS

%I #29 Mar 24 2016 16:42:26

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

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

%U 0,1

%N Decimal expansion of sqrt(1+2*sqrt(3+4*sqrt(5+6*sqrt(7+...)))).

%H Charles R Greathouse IV, <a href="/A254689/b254689.txt">Table of n, a(n) for n = 1..10000</a>

%e 3.59854454068856909259879177588536401075721686476680448902107357530370181023113...

%o (PARI) /* This program approximates the constant using the first n radicals. If n is omitted it attempts to compute the constant to within 1 ulp at the current precision. */

%o approx(n=default(realprecision)\.3+9)=my(t=2*n+5-5/n); forstep(k=2*n,2,-2, t=sqrt(k-1+k*t)); t \\ _Charles R Greathouse IV_, Mar 24 2016

%K nonn,cons

%O 1,1

%A _Johannes Røsok Eskilt_, Mar 24 2016

%E a(17)-a(70) from _Charles R Greathouse IV_, Mar 24 2016