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A066658 Denominators of rational numbers produced in order by A066720(j)/A066720(i) for i >= 1, 1 <= j

%I A066658 #11 Aug 23 2022 13:08:29
%S A066658 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,
%T A066658 13,17,17,17,17,17,17,17,17,18,9,6,18,18,9,18,18,18,19,19,19,19,19,19,
%U A066658 19,19,19,19,23,23,23,23,23,23,23,23,23,23,23,29,29
%N A066658 Denominators of rational numbers produced in order by A066720(j)/A066720(i) for i >= 1, 1 <= j <i.
%C A066658 Does every rational number in range (0,1) appear?
%C A066658 a(0) = 1 by convention.
%H A066658 Reinhard Zumkeller, <a href="/A066658/b066658.txt">Table of n, a(n) for n = 0..10000</a>
%e A066658 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, ...
%t A066658 nmax = 14;
%t A066658 b[1] = 1; F = {1};
%t A066658 For[n = 2, n <= nmax, n++,
%t A066658 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[]]]];
%t A066658 Join[{1}, Table[b[k]/b[n], {n, 1, nmax}, {k, 1, n - 1}]] // Flatten // Denominator (* _Jean-François Alcover_, Aug 23 2022, after _Robert Israel_ in A066720 *)
%o A066658 (Haskell)
%o A066658 import Data.List (inits)
%o A066658 import Data.Ratio ((%), denominator)
%o A066658 a066658 n = a066658_list !! n
%o A066658 a066658_list = map denominator
%o A066658    (1 : (concat $ tail $ zipWith (\u vs -> map (% u) vs)
%o A066658                                  a066720_list (inits a066720_list)))
%o A066658 -- _Reinhard Zumkeller_, Nov 19 2013
%Y A066658 Cf. A066657 (numerators), A066720.
%K A066658 nonn,frac,nice
%O A066658 0,2
%A A066658 _N. J. A. Sloane_, Jan 18 2002