A156649 Decimal expansion of (9+4*sqrt(2))/7.

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

Offset

1,1

Comments

Limit_{n -> oo} b(n)/b(n-1) = ((9+4*sqrt(2))/7)/((19+6*sqrt(2))/17) for n mod 9 = {1, 2}, b = A129837, A156650.

The aspect ratio of a rectangle such that a random line intersecting it has a 1/2 probability of intersecting two opposite sides. The line is chosen such that its orientation and its perpendicular distance from the origin are independently and uniformly distributed. - Amiram Eldar, Apr 30 2026

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 2.

Formula

Minimal polynomial: 7*x^2 - 18*x + 7. - Amiram Eldar, Apr 30 2026

Example

2.09383632135605431360096498526268461632552678592968...

Mathematica

RealDigits[(9 + 4*Sqrt[2])/7, 10, 100][[1]] (* G. C. Greubel, Jul 05 2017 *)

Prog

(PARI) (9+4*sqrt(2))/7 \\ G. C. Greubel, Jul 05 2017

Crossrefs

Cf. A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A156163 (decimal expansion of (19+6*sqrt(2))/17), A129837, A156650.

Sequence in context: A071120 A249417 A189963 * A197330 A395758 A343882

Adjacent sequences: A156646 A156647 A156648 * A156650 A156651 A156652

Keyword

cons,nonn

Author

Klaus Brockhaus, Feb 13 2009

Status

approved