A188945 - OEIS

A188945

Decimal expansion of (4+sqrt(7))/3.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Decimal expansion of the shape (= length/width = (4+sqrt(7))/3) of the greater (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

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

EXAMPLE

2.215250437021530196833871917879753475236753061...

MATHEMATICA

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

N[t, 130]

RealDigits[N[t, 130]][[1]]

ContinuedFraction[t, 120]

RealDigits[(4+Sqrt[7])/3, 10, 150][[1]] (* Harvey P. Dale, Jan 23 2026 *)

CROSSREFS

Cf. A188738, A188944.