A317988 Farey fraction tree, reading each fraction's numerator first, then its denominator.

0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 4, 1, 5, 2, 5, 3, 5, 4, 5, 1, 6, 5, 6, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 7, 1, 8, 3, 8, 5, 8, 7, 8, 1, 9, 2, 9, 4, 9, 5, 9, 7, 9, 8, 9, 1, 10, 3, 10, 7, 10, 9, 10, 1, 11, 2, 11, 3, 11, 4, 11, 5, 11, 6, 11, 7, 11, 8, 11, 9, 11, 10, 11, 1, 12, 5, 12, 7, 12, 11, 12

Offset: 1

Author

Robert G. Wilson v, Oct 03 2018

Keywords

• nonn

Comments

0 < a(2n-1)/a(2n) < 1 for n > 2.

This appears to be A038568 preceded by 0,1,1. - Peter Kagey, Jan 09 2022

Examples

			Farey fraction tree begins:
  0/1                                             1/1
                          1/2
                  1/3             2/3
              1/4                     3/4
           1/5       2/5       3/5       4/5
          1/6                             5/6
         1/7    2/7    3/7   4/7    5/7    6/7
        1/8         3/8         5/8         7/8
       1/9   2/9       4/9   5/9       7/9   8/9
      1/10      3/10                7/10     9/10
  ...
		

Crossrefs

Cf. A038566, A038567, A038568.

Programs

Mathematica

Table[ If[ GCD[n, d] == 1, {n, d}, {}], {d, 0, 12}, {n, 0, d}] // Flatten

Formula

0,1 followed by the interleaving of A038566 & A038567.