

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+1j.


4



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
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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



