OFFSET
1,1
EXAMPLE
First 5 rows:
5 ... 8
5 ... 8 ... 12
5 ... 8 ... 40 .. 85
5 ... 8 ... 12 .. 96 .. 221 . 480
5 ... 8 ... 145 . 260 . 533. 1160 . 1300 . 2813
The following list shows for n = 3 the purely periodic continued fractions (with period an n-tuple of 1s and 2s), each followed by the number r it represents, the minimal polynomial a*x^2 + b*x + c of r, and the discriminant, D = b^2 - 4*a*c.
[(1,1,1)] = (1+sqrt(5))/2, -1 - x + x^2, D = 5
[(1,1,2)] = sqrt(10)/4, -5 + 2 x^2, D = 40
[(1,2,1)] = (2 + sqrt(10)/3, -2 - 4 x + 3 x^2, D = 10
[(2,1,1)] = (1 + sqrt(85))/6, -7 - x + 3 x^2, D = 85
[(1,2,2)] = (1 + sqrt(10)/3, -3 - 2 x + 3 x^2, D = 10
[(2,1,2)] = (-1 + sqrt(85))/6, -7 + x + 3 x^2, D = 85
[(2,2,2)] = (5 + sqrt(85))/10, -3 - 5 x + 5 x^2, D = 85
[(2,2,2)] = sqrt(2), -2 + x^2, D = 8
The distinct values of D are 5, 8, 10, 85, as in row 3.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Clark Kimberling, Sep 06 2014
STATUS
approved