A066658 - OEIS

%I #11 Aug 23 2022 13:08:29

%S 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 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 19,19,19,19,23,23,23,23,23,23,23,23,23,23,23,29,29

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

%C Does every rational number in range (0,1) appear?

%C a(0) = 1 by convention.

%H Reinhard Zumkeller, <a href="/A066658/b066658.txt">Table of n, a(n) for n = 0..10000</a>

%e 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 nmax = 14;

%t b[1] = 1; F = {1};

%t For[n = 2, n <= nmax, n++,

%t 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 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 (Haskell)

%o import Data.List (inits)

%o import Data.Ratio ((%), denominator)

%o a066658 n = a066658_list !! n

%o a066658_list = map denominator

%o    (1 : (concat $ tail $ zipWith (\u vs -> map (% u) vs)

%o                                  a066720_list (inits a066720_list)))

%o -- _Reinhard Zumkeller_, Nov 19 2013

%Y Cf. A066657 (numerators), A066720.

%K nonn,frac,nice

%O 0,2

%A _N. J. A. Sloane_, Jan 18 2002