A259911 Triangular array; row k shows the discriminant of the field of the number having purely periodic continued fraction with period (j,k), for j=1..k+1-j.

5, 12, 12, 21, 8, 21, 8, 60, 60, 8, 5, 24, 13, 24, 5, 60, 140, 12, 12, 140, 60, 77, 12, 285, 5, 285, 12, 77, 24, 28, 44, 120, 120, 44, 28, 24, 13, 5, 21, 168, 29, 168, 21, 5, 13, 140, 44, 168, 56, 1020, 1020, 56, 168, 44, 140, 165, 120, 93, 8, 1365, 40, 1365

Offset

1,1

Comments

The number whose continued fraction is periodic with period (1,1) is the golden ratio, (1+sqrt(5))/2, so that the number in row 1 is 5.

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

First eight rows:
5
12    12
21    8     21
8     60    60    8
5     24    13    24    5
60    140   12    12    140   60
77    12    285   5     285   12    77
24    28    44    120   120   44    28    24

Mathematica

v = Table[FromContinuedFraction[{j, {k + 1 - j, j}}], {k, 1, 20}, {j, 1, k}];
TableForm[NumberFieldDiscriminant[v]]

Crossrefs

Cf. A259912.

Sequence in context: A251935 A195031 A265028 * A259860 A268035 A223255

Adjacent sequences: A259908 A259909 A259910 * A259912 A259913 A259914

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Jul 20 2015

Status

approved