A298814 Decimal expansion of the greatest real zero of x^8 - 2*x^4 - x + 1.

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

Offset

1,2

Comments

Let (d(n)) = (0,0,1,0,0,1,...), s(n) = (s(n-1) + d(n))^(1/2) for n > 0, and s(0) = 1.

Then s(3n) -> 1.096981557798..., as in A230161;

s(3n+1) -> 1.2033685381501..., as in A298814;

s(3n+2) -> 1.44809583860..., as in A298815.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

Greatest real zero = 1.2033685381501...

Mathematica

r = x /. NSolve[x^8 - 2 x^4 - x + 1 == 0, x, 10000][[8]];
RealDigits[r][[1]]; (* A298814 *)

Prog

(PARI) solve(x=1, 2, x^8 - 2*x^4 - x + 1) \\ Michel Marcus, Nov 05 2018

Crossrefs

Cf. A230161, A298813, A298815.

Sequence in context: A343762 A247508 A112239 * A343980 A021835 A112476

Adjacent sequences: A298811 A298812 A298813 * A298815 A298816 A298817

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 13 2018

Status

approved