A066657 - OEIS

%I #12 Aug 23 2022 13:08:24

%S 1,1,1,2,1,2,3,1,2,3,5,1,1,3,5,7,1,2,3,5,7,8,1,2,3,5,7,8,11,1,2,3,5,7,

%T 8,11,13,1,1,1,5,7,4,11,13,17,1,2,3,5,7,8,11,13,17,18,1,2,3,5,7,8,11,

%U 13,17,18,19,1,2,3,5,7,8,11,13,17,18,19,23,1,2,3,5,7

%N Numerators 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="/A066657/b066657.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 // Numerator (* _Jean-François Alcover_, Aug 23 2022, after _Robert Israel in A066720 *)

%o (Haskell)

%o import Data.List (inits)

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

%o a066657 n = a066657_list !! n

%o a066657_list = map numerator

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

%o                                  a066720_list (inits a066720_list)))

%o -- _Reinhard Zumkeller_, Nov 19 2013

%Y Cf. A066658 (denominators), A066720.

%K nonn,frac,nice

%O 0,4

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