A188944 Decimal expansion of (4-sqrt(7))/3.

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

Offset

0,1

Comments

Decimal expansion of the shape (= length/width = (4-sqrt(7))/3) of the lesser (8/3)-contraction rectangle.

See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.

Links

Table of n, a(n) for n=0..129.

Index entries for algebraic numbers, degree 2.

Formula

Minimal polynomial: 3*x^2 - 8*x + 3. - Amiram Eldar, Jun 08 2026

Example

0.45141622964513646983279474878691319142991360...

Mathematica

r = 8/3; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]

Prog

(PARI) (4-sqrt(7))/3 \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A188738, A188945.

Sequence in context: A379057 A070769 A021693 * A010662 A390690 A385628

Adjacent sequences: A188941 A188942 A188943 * A188945 A188946 A188947

Keyword

nonn,cons,easy,changed

Author

Clark Kimberling, Apr 14 2011

Status

approved