A212695 Decimal expansion of the uniform exponent of simultaneous approximation of Q-linearly independent triples (1,x,x^3) by rational numbers.

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

Offset

0,1

Links

Table of n, a(n) for n=0..100.

Stéphane Lozier and Damien Roy, Simultaneous approximation to a real number and to its cube, arXiv:1205.5041v1 [math.NT], May 22, 2012.

Index entries for algebraic numbers, degree 2.

Formula

Equals (9+sqrt(11))/35.

Minimal polynomial: 35*x^2 - 18*x + 2. - Amiram Eldar, Jun 11 2026

Example

0.3519035654387257...

Mathematica

RealDigits[(9 + Sqrt[11])/35, 10, 105][[1]] (* T. D. Noe, May 24 2012 *)

Crossrefs

Sequence in context: A340529 A197326 A235605 * A209422 A361944 A320386

Adjacent sequences: A212692 A212693 A212694 * A212696 A212697 A212698

Keyword

nonn,cons,easy

Author

Jonathan Vos Post, May 23 2012

Status

approved