

A298853


Decimal expansion of the greatest real zero of x^4  2*x^2  x  1.


2



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

1,2


COMMENTS

Let (d(n)) = (2,1,2,1,2,1,...), s(n) = (s(n1) + d(n))^(1/2) for n > 0, and s(0) = 1.
Then s(2n) > 1.9263032199..., as in A298852;
s(2n+1) > 1.710644095..., as in A298853.


LINKS



EXAMPLE

Greatest real zero = 1.710644095...


MATHEMATICA

r = x /. NSolve[x^4  2 x^2  x  1 == 0, x, 10000][[4]];
RealDigits[Root[ x^42*x^2x1, 2], 10, 120][[1]] (* Harvey P. Dale, May 23 2019 *)


PROG

(PARI) solve(x=1, 2, x^42*x^2x1) \\ Michel Marcus, Apr 14 2020


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



