Re: unit numbers** to ratios

Here's another. It's been a couple of years or more since I wrote the
program, and I am fuzzy on the details, but I used Euclid's algorithm to get
approximations. My goal was to use the smallest primes possible and still
come up with a decent approximation:

2 et 1/1 3/2

3 et 1/1 5/4 3/2

4 et 1/1 6/5 3/2 5/3

5 et 1/1 8/7 4/3 3/2 7/4

6 et 1/1 9/8 5/4 3/2 8/5 7/4

7 et 1/1 10/9 5/4 4/3 3/2 5/3 9/5

8 et 1/1 12/11 6/5 4/3 7/5 3/2 5/3 11/6

9 et 1/1 13/12 7/6 5/4 4/3 3/2 8/5 5/3 13/7

10 et 1/1 15/14 8/7 5/4 4/3 7/5 3/2 5/3 7/4 13/7

11 et 1/1 16/15 8/7 6/5 9/7 4/3 3/2 14/9 5/3 7/4 15/8

12 et 1/1 18/17 9/8 6/5 5/4 4/3 7/5 3/2 8/5 5/3 7/4 17/9

13 et 1/1 19/18 10/9 7/6 5/4 4/3 11/8 16/11 3/2 8/5 5/3 9/5 19/10

14 et 1/1 21/20 10/9 7/6 5/4 9/7 4/3 7/5 3/2 11/7 5/3 7/4 9/5 19/10

15 et 1/1 22/21 11/10 8/7 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 7/4 11/6 21/11

16 et 1/1 23/22 12/11 8/7 6/5 5/4 13/10 4/3 7/5 3/2 17/11 8/5 5/3 7/4 11/6
23/12

17 et 1/1 25/24 13/12 9/8 7/6 5/4 9/7 4/3 7/5 13/9 3/2 11/7 13/8 5/3 7/4 11/6
23/12

18 et 1/1 26/25 13/12 9/8 7/6 6/5 5/4 4/3 15/11 7/5 25/17 3/2 8/5 5/3 12/7 7/4
13/7 25/13

19 et 1/1 28/27 14/13 10/9 7/6 6/5 5/4 9/7 4/3 7/5 13/9 3/2 14/9 8/5 5/3 7/4
9/5 13/7 27/14

20 et 1/1 29/28 15/14 10/9 8/7 6/5 5/4 14/11 4/3 15/11 7/5 19/13 3/2 11/7 13/8
5/3 7/4 9/5 13/7 29/15

21 et 1/1 31/30 16/15 10/9 8/7 6/5 11/9 5/4 13/10 4/3 7/5 10/7 3/2 20/13 8/5
5/3 17/10 7/4 9/5 15/8 29/15

22 et 1/1 32/31 16/15 11/10 8/7 7/6 6/5 5/4 9/7 4/3 11/8 7/5 19/13 3/2 14/9
8/5 5/3 12/7 7/4 9/5 15/8 31/16

23 et 1/1 34/33 17/16 11/10 9/8 7/6 6/5 5/4 14/11 21/16 4/3 7/5 10/7 3/2 29/19
11/7 13/8 5/3 12/7 7/4 11/6 15/8 33/17

24 et 1/1 35/34 18/17 12/11 9/8 7/6 6/5 11/9 5/4 13/10 4/3 11/8 7/5 16/11 3/2
17/11 8/5 18/11 5/3 7/4 16/9 11/6 17/9 33/17

25 et 1/1 36/35 18/17 12/11 9/8 8/7 13/11 6/5 5/4 9/7 4/3 19/14 7/5 10/7 28/19
3/2 14/9 8/5 5/3 22/13 7/4 9/5 11/6 17/9 35/18

26 et 1/1 38/37 19/18 13/12 10/9 8/7 7/6 6/5 5/4 14/11 17/13 4/3 11/8 7/5
16/11 3/2 23/15 11/7 8/5 5/3 12/7 7/4 9/5 11/6 19/10 37/19

27 et 1/1 39/38 20/19 13/12 10/9 8/7 7/6 6/5 11/9 5/4 9/7 4/3 15/11 7/5 10/7
25/17 3/2 17/11 8/5 13/8 5/3 12/7 7/4 9/5 13/7 19/10 39/20

28 et 1/1 41/40 21/20 14/13 10/9 8/7 7/6 6/5 11/9 5/4 9/7 21/16 4/3 11/8 7/5
13/9 3/2 32/21 11/7 8/5 18/11 5/3 19/11 7/4 9/5 13/7 19/10 39/20

29 et 1/1 42/41 21/20 14/13 11/10 9/8 7/6 13/11 6/5 5/4 14/11 13/10 4/3 15/11
7/5 10/7 22/15 3/2 20/13 11/7 8/5 5/3 22/13 7/4 16/9 9/5 13/7 21/11 41/21

30 et 1/1 44/43 22/21 15/14 11/10 9/8 8/7 7/6 6/5 16/13 5/4 9/7 4/3 27/20 11/8
7/5 13/9 40/27 3/2 14/9 8/5 13/8 5/3 17/10 7/4 16/9 11/6 13/7 21/11 43/22

31 et 1/1 45/44 23/22 15/14 12/11 9/8 8/7 7/6 6/5 11/9 5/4 9/7 17/13 4/3 11/8
7/5 10/7 19/13 3/2 26/17 11/7 8/5 18/11 5/3 12/7 7/4 9/5 11/6 15/8 21/11 43/22