A230154 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=6.

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

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=-6.

Examples

			0.8986537126286992932608757220468058862604482200934396966...
		

Links

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

Crossrefs

Cf. A075778, A230151, A230152, A230153, A230155, A230156, A230157, A230158, A230160, A377081.

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,-6);

Mathematica

RealDigits[x/.FindRoot[x^7+x^6==1,{x,1},WorkingPrecision->120]][[1]] (* Harvey P. Dale, Dec 30 2013 *)

Formula

Equals 1/A230160. - Hugo Pfoertner, Oct 15 2024