A230157 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=9.

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

Offset: 0

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

			0.9295701282320228642044130369144641254353258530020248336...
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A075778, A230151-A230156, A230158.

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[x^10 + x^9 - 1, 2] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)