A066657 Numerators of rational numbers produced in order by A066720(j)/A066720(i) for i >= 1, 1 <= j

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

Offset: 0

Author

N. J. A. Sloane, Jan 18 2002

Keywords

• nonn
• frac
• nice

Comments

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

a(0) = 1 by convention.

Examples

			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, ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A066658 (denominators), A066720.

Programs

Haskell

import Data.List (inits)
import Data.Ratio ((%), numerator)
a066657 n = a066657_list !! n
a066657_list = map numerator
   (1 : (concat $ tail $ zipWith (\u vs -> map (% u) vs)
                                 a066720_list (inits a066720_list)))
-- Reinhard Zumkeller, Nov 19 2013

Mathematica

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[]]]];
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 *)