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A259911
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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.
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4
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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v = Table[FromContinuedFraction[{j, {k + 1 - j, j}}], {k, 1, 20}, {j, 1, k}];
TableForm[NumberFieldDiscriminant[v]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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