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%I #17 Mar 03 2023 22:33:21
%S 1,1,1,2,7,7,5,6,8,4,2,7,8,7,0,5,4,7,0,6,2,9,7,0,4,0,2,0,5,7,1,0,9,2,
%T 9,3,5,6,0,6,8,5,9,2,7,1,8,5,5,2,8,3,6,8,1,4,8,5,7,0,1,6,2,8,0,0,7,1,
%U 6,6,3,3,2,5,7,9,5,2,8,4,4,3,4,5,9,2,7
%N Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=7.
%C Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=7.
%H Paolo P. Lava, <a href="/A230160/b230160.txt">Table of n, a(n) for n = 1..1000</a> (corrected by _Sean A. Irvine_)
%e 1.1127756842787054706297040205710929356068592718552836814...
%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(1000,7);
%t Root[x^7 - x - 1, 1] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y Cf. A001622, A060006, A060007, A160155, A230159, A230161-A230163.
%K nonn,cons
%O 1,4
%A _Paolo P. Lava_, Oct 11 2013
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