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A066658
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Denominators of rational numbers produced in order by A066720(j)/A066720(i) for i >= 1, 1 <= j <i.
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8
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1, 2, 3, 3, 5, 5, 5, 7, 7, 7, 7, 8, 4, 8, 8, 8, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 18, 9, 6, 18, 18, 9, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29
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OFFSET
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0,2
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COMMENTS
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Does every rational number in range (0,1) appear?
a(0) = 1 by convention.
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LINKS
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EXAMPLE
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Sequence of rationals begins 1, 1/2, 1/3, 2/3, 1/5, 2/5, 3/5, 1/7, 2/7, 3/7, 5/7, 1/8, 1/4, 3/8, 5/8, 7/8, 1/11, 2/11, ...
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MATHEMATICA
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nmax = 14;
b[1] = 1; F = {1};
For[n = 2, n <= nmax, n++,
For[k = b[n - 1] + 1, True, k++, Fk = Join[{k^2}, Table[b[i]*k, {i, 1, n - 1}]] // Union; If[Fk~Intersection~F == {}, b[n] = k; F = F~Union~Fk; Break[]]]];
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PROG
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(Haskell)
import Data.List (inits)
import Data.Ratio ((%), denominator)
a066658 n = a066658_list !! n
a066658_list = map denominator
(1 : (concat $ tail $ zipWith (\u vs -> map (% u) vs)
a066720_list (inits a066720_list)))
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CROSSREFS
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KEYWORD
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nonn,frac,nice
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AUTHOR
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STATUS
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approved
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