%I #13 Dec 05 2016 10:40:33

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

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

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

%N Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=8.

%C Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=8.

%H Paolo P. Lava, <a href="/A230161/b230161.txt">Table of n, a(n) for n = 1..1000</a>

%e 1.0969815577985598179082789671675370895925301082127867138...

%p with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);

%p for n from q by -1 to 1 do a:=(1+a)^(1/h);od;

%p print(evalf(a,1000)); end: P(1000,8);

%t Root[x^8 - x - 1, 2] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)

%Y Cf. A001622, A060006, A060007, A160155, A230159, A230160, A230162, A230163.

%K nonn,cons

%O 1,3

%A _Paolo P. Lava_, Oct 11 2013