A230162 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=9.

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

Author

Paolo P. Lava, Oct 11 2013

Keywords

• nonn
• cons

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=9.

Examples

			1.0850702454914508283368958640973142340506536310308965814...
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001622, A060006, A060007, A160155, A230159-A230161, A230163.

Programs

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 *)