

A117605


Decimal expansion of the real solution to equation x^3 + 3*x = 2.


4



5, 9, 6, 0, 7, 1, 6, 3, 7, 9, 8, 3, 3, 2, 1, 5, 2, 3, 1, 1, 2, 8, 0, 5, 4, 1, 4, 3, 9, 9, 6, 8, 1, 8, 2, 8, 1, 1, 3, 3, 2, 5, 4, 9, 4, 3, 9, 6, 2, 1, 3, 1, 9, 4, 3, 2, 4, 7, 9, 0, 8, 3, 0, 3, 6, 0, 0, 5, 1, 6, 2, 6, 8, 6, 2, 0, 8, 9, 1, 8, 5, 8, 7, 1, 6, 6, 0, 3, 3, 7, 5, 4, 2, 8, 4, 7, 5, 4, 7, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

A014176 Decimal expansion of the silver mean, 1+sqrt(2). Interestingly, when we look for x=0.596071637983321523112805414399681828113325, the original Inverse Symbolic Calculator replies: "... Roots of polynomials of 4th degree (coeffs: 9..9) 5960716379833215 = 10+15*x+5*x^3"  with wrong sign of the first term.
Let p(n,x) denote the nth Maclaurin polynomial of e^x, and let p'(n,x) denote its derivative. Then p'(n+1,x) = p(n,x), so that the real zero r of p(n,x), for odd n, is also the value of x that minimizes p(n+1,x). Let y = 0.5960716... . Then for n = 3, we have r =  y  1; see A332324 for the minimal value of p(4,x).  Clark Kimberling, Feb 13 2020


LINKS

Table of n, a(n) for n=0..99.
Original Inverse Symbolic Calculator


FORMULA

x = (1+sqrt(2))^(1/3)  1/(1+sqrt(2))^(1/3).


EXAMPLE

x = 0.596071637983321523112805414399681828113325...


MATHEMATICA

RealDigits[N[Solve[3*z+z^3==2, z][[1, 1, 2]], 100]][[1]]


CROSSREFS

Cf. A014176, A332324.
Sequence in context: A133742 A134879 A051158 * A303983 A073003 A087498
Adjacent sequences: A117602 A117603 A117604 * A117606 A117607 A117608


KEYWORD

cons,nonn


AUTHOR

Zak Seidov, Apr 27 2006


EXTENSIONS

Website URL and name (changed from "Plouffe's Inverter") updated by Jon E. Schoenfield, Feb 28 2020


STATUS

approved



