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A230162
Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=9.
4
1, 0, 8, 5, 0, 7, 0, 2, 4, 5, 4, 9, 1, 4, 5, 0, 8, 2, 8, 3, 3, 6, 8, 9, 5, 8, 6, 4, 0, 9, 7, 3, 1, 4, 2, 3, 4, 0, 5, 0, 6, 5, 3, 6, 3, 1, 0, 3, 0, 8, 9, 6, 5, 8, 1, 4, 6, 8, 6, 1, 5, 5, 3, 3, 3, 6, 5, 1, 8, 0, 4, 9, 9, 4, 0, 1, 1, 5, 7, 1, 9, 9, 7, 4, 1, 9, 3
OFFSET
1,3
COMMENTS
Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=9.
LINKS
EXAMPLE
1.0850702454914508283368958640973142340506536310308965814...
MAPLE
with(numtheory); P:=proc(q, h) local a, n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h); od;
print(evalf(a, 1000)); end: P(1000, 9);
MATHEMATICA
Root[(#^9-#-1)&, 1] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[x/.FindRoot[x^9-x-1==0, {x, 1}, WorkingPrecision->100]][[1]] (* Harvey P. Dale, Jul 31 2017 *)
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Oct 11 2013
STATUS
approved