A230151 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=3.

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

Offset

0,1

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-3.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000 (corrected by Sean A. Irvine)

Example

0.8191725133961644396995711883424270403484978325537129656...

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, -3);

Mathematica

Root[(#^4+#^3-1)&, 2] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

Crossrefs

Cf. A086106 (other real root).

Cf. A075778, A230152-A230158.

Sequence in context: A133820 A258718 A019864 * A308043 A286253 A198674

Adjacent sequences: A230148 A230149 A230150 * A230152 A230153 A230154

Keyword

nonn,cons

Author

Paolo P. Lava, Oct 11 2013

Status

approved