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A259911
Triangular array; row k shows the discriminant of the field of the number having purely periodic continued fraction with period (j,k+1-j), for j=1..k.
5
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, 8, 93, 120, 165
OFFSET
1,1
LINKS
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
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.
As a square array A(n,k) read by antidiagonals, where A(n,k) corresponds to the continued fraction with pure period (n,k):
5, 12, 21, 8, 5, 60, 77, 24, ...
12, 8, 60, 24, 140, 12, 28, 5, ...
21, 60, 13, 12, 285, 44, 21, 168, ...
8, 24, 12, 5, 120, 168, 56, 8, ...
5, 140, 285, 120, 29, 1020, 1365, 440, ...
60, 12, 44, 168, 1020, 40, 1932, 156, ...
77, 28, 21, 56, 1365, 1932, 53, 840, ...
24, 5, 168, 8, 440, 156, 840, 17, ...
...
MATHEMATICA
v = Table[FromContinuedFraction[{j, {k + 1 - j, j}}], {k, 1, 20}, {j, 1, k}];
TableForm[NumberFieldDiscriminant[v]]
CROSSREFS
Cf. A259912 (main diagonal of square array), A259913 (first column).
Sequence in context: A251935 A195031 A265028 * A259860 A268035 A223255
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Jul 20 2015
STATUS
approved