User:Flirora/Independent generators
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Given a tuning in which the interval of equivalence is divided into N equal parts, two generators m\N and n\N are independent if:
- gcd(m, N) = gcd(n, N) = 1 (both generators can reach all pitch classes when stacked iteratively)
- in the pairs (m, n), (m, N − n), (N − m, n), and (N − m, N − n), neither integer divides the other (that is, neither interval or its complement can be taken as a multiple of the other or its complement)
Implementation in Raku:
->\n {grep {my@a=.map({$_&n-$_});2>.all gcd n&&@a[0]%@a[1]&@a[1]%@a[0]&[<] $_},[X] (3..n/2)xx 2}
List
| N | Independent pairs |
|---|---|
| 1 | none |
| 2 | none |
| 3 | none |
| 4 | none |
| 5 | none |
| 6 | none |
| 7 | none |
| 8 | none |
| 9 | none |
| 10 | none |
| 11 | (4, 5) |
| 12 | none |
| 13 | (4, 6) (5, 6) |
| 14 | none |
| 15 | none |
| 16 | (3, 5) (5, 7) |
| 17 | (3, 4) (4, 6) (4, 7) (5, 8) (6, 7) (6, 8) (7, 8) |
| 18 | (5, 7) |
| 19 | (3, 5) (4, 6) (4, 9) (5, 6) (5, 8) (6, 8) (6, 9) (7, 8) (7, 9) (8, 9) |
| 20 | (3, 7) (7, 9) |
| 21 | (4, 10) (8, 10) |
| 22 | (3, 5) (5, 9) (7, 9) |
| 23 | (3, 7) (4, 5) (4, 6) (4, 9) (4, 10) (5, 7) (5, 11) (6, 7) (6, 8) (6, 9) (6, 10) (7, 10) (7, 11) (8, 9) (8, 10) (8, 11) (9, 10) (9, 11) (10, 11) |
| 24 | (5, 7) (5, 11) (7, 11) |
| 25 | (3, 8) (4, 6) (4, 11) (6, 8) (6, 9) (6, 11) (7, 8) (7, 12) (8, 11) (8, 12) (9, 11) (9, 12) (11, 12) |
| 26 | (3, 7) (5, 9) (7, 9) (7, 11) (9, 11) |
| 27 | (4, 5) (4, 10) (4, 13) (5, 8) (5, 13) (7, 8) (7, 11) (8, 10) (8, 13) (10, 11) (10, 13) (11, 13) |
| 28 | (3, 11) (5, 9) (5, 11) (9, 11) (9, 13) (11, 13) |
| 29 | (3, 4) (3, 7) (3, 10) (4, 6) (4, 7) (4, 10) (4, 11) (4, 14) (5, 7) (5, 11) (5, 13) (6, 7) (6, 8) (6, 9) (6, 10) (6, 13) (6, 14) (7, 9) (7, 10) (7, 12) (7, 13) (8, 9) (8, 10) (8, 11) (8, 12) (8, 14) (9, 12) (9, 13) (9, 14) (10, 11) (10, 12) (10, 13) (10, 14) (11, 12) (11, 13) (11, 14) (12, 13) (12, 14) (13, 14) |
| 30 | (7, 11) (7, 13) (11, 13) |
| 31 | (3, 5) (3, 8) (3, 11) (4, 5) (4, 6) (4, 10) (4, 13) (4, 14) (5, 7) (5, 8) (5, 9) (5, 12) (5, 14) (6, 8) (6, 9) (6, 10) (6, 11) (6, 14) (6, 15) (7, 9) (7, 11) (7, 13) (7, 15) (8, 9) (8, 10) (8, 11) (8, 12) (8, 13) (8, 14) (9, 10) (9, 12) (9, 14) (9, 15) (10, 12) (10, 13) (10, 14) (10, 15) (11, 12) (11, 13) (11, 14) (11, 15) (12, 13) (12, 14) (12, 15) (13, 14) (13, 15) (14, 15) |
| 32 | (3, 7) (3, 13) (5, 11) (5, 13) (7, 9) (7, 13) (7, 15) (9, 11) (9, 13) (9, 15) (11, 13) (11, 15) (13, 15) |
| 33 | (4, 7) (4, 10) (4, 14) (5, 16) (7, 8) (7, 10) (7, 16) (8, 10) (8, 13) (8, 14) (10, 14) (10, 16) (13, 14) (13, 16) (14, 16) |
| 34 | (3, 5) (3, 11) (5, 7) (5, 11) (5, 13) (7, 11) (7, 15) (9, 11) (9, 13) (9, 15) (11, 13) (11, 15) (13, 15) |
| 35 | (3, 13) (4, 6) (4, 9) (4, 13) (4, 17) (6, 8) (6, 9) (6, 13) (6, 16) (8, 12) (8, 13) (8, 17) (9, 11) (9, 12) (9, 16) (11, 16) (11, 17) (12, 13) (12, 16) (12, 17) (13, 16) (13, 17) (16, 17) |
| 36 | (5, 7) (5, 13) (5, 17) (7, 11) (7, 13) (7, 17) (11, 13) (11, 17) (13, 17) |
| 37 | (3, 5) (3, 8) (3, 11) (3, 14) (4, 6) (4, 7) (4, 10) (4, 14) (4, 15) (4, 18) (5, 6) (5, 9) (5, 11) (5, 13) (5, 14) (5, 18) (6, 8) (6, 9) (6, 10) (6, 11) (6, 14) (6, 15) (6, 16) (6, 17) (7, 8) (7, 11) (7, 12) (7, 13) (7, 17) (7, 18) (8, 9) (8, 10) (8, 11) (8, 12) (8, 14) (8, 15) (8, 17) (8, 18) (9, 11) (9, 12) (9, 13) (9, 15) (9, 16) (9, 17) (10, 11) (10, 12) (10, 13) (10, 14) (10, 15) (10, 16) (10, 18) (11, 12) (11, 14) (11, 16) (11, 17) (11, 18) (12, 14) (12, 15) (12, 16) (12, 17) (12, 18) (13, 14) (13, 15) (13, 16) (13, 17) (13, 18) (14, 15) (14, 16) (14, 17) (14, 18) (15, 16) (15, 17) (15, 18) (16, 17) (16, 18) (17, 18) |
| 38 | (3, 13) (5, 7) (5, 9) (5, 17) (7, 9) (7, 11) (7, 13) (7, 15) (9, 13) (9, 15) (9, 17) (11, 13) (11, 15) (11, 17) (13, 15) (13, 17) (15, 17) |
| 39 | (4, 10) (4, 14) (4, 17) (5, 7) (5, 8) (5, 11) (5, 16) (7, 10) (7, 17) (7, 19) (8, 10) (8, 11) (8, 14) (8, 17) (8, 19) (10, 11) (10, 14) (10, 16) (10, 17) (11, 16) (11, 19) (14, 16) (14, 17) (14, 19) (16, 17) (16, 19) (17, 19) |
| 40 | (3, 11) (3, 17) (7, 9) (7, 13) (7, 17) (9, 11) (9, 17) (9, 19) (11, 13) (11, 17) (11, 19) (13, 17) (13, 19) (17, 19) |
| 41 | (3, 4) (3, 7) (3, 10) (3, 13) (3, 16) (4, 6) (4, 7) (4, 10) (4, 11) (4, 14) (4, 15) (4, 18) (4, 19) (5, 7) (5, 8) (5, 13) (5, 14) (5, 17) (5, 19) (6, 8) (6, 9) (6, 10) (6, 13) (6, 14) (6, 15) (6, 16) (6, 19) (6, 20) (7, 8) (7, 9) (7, 10) (7, 11) (7, 12) (7, 15) (7, 16) (7, 18) (7, 19) (8, 10) (8, 12) (8, 13) (8, 14) (8, 15) (8, 18) (8, 19) (8, 20) (9, 10) (9, 11) (9, 12) (9, 13) (9, 15) (9, 17) (9, 19) (9, 20) (10, 12) (10, 13) (10, 14) (10, 15) (10, 16) (10, 17) (10, 18) (10, 19) (11, 12) (11, 13) (11, 14) (11, 16) (11, 17) (11, 18) (11, 20) (12, 13) (12, 14) (12, 15) (12, 16) (12, 18) (12, 19) (12, 20) (13, 16) (13, 17) (13, 18) (13, 19) (13, 20) (14, 15) (14, 16) (14, 17) (14, 18) (14, 19) (14, 20) (15, 16) (15, 17) (15, 18) (15, 19) (15, 20) (16, 17) (16, 18) (16, 19) (16, 20) (17, 18) (17, 19) (17, 20) (18, 19) (18, 20) (19, 20) |
| 42 | (5, 11) (5, 13) (5, 19) (11, 13) (11, 17) (11, 19) (13, 17) (13, 19) (17, 19) |
| 43 | (3, 11) (3, 14) (3, 17) (4, 5) (4, 6) (4, 9) (4, 10) (4, 14) (4, 17) (4, 18) (4, 21) (5, 6) (5, 7) (5, 9) (5, 11) (5, 12) (5, 14) (5, 16) (5, 17) (5, 21) (6, 8) (6, 9) (6, 10) (6, 11) (6, 14) (6, 15) (6, 16) (6, 17) (6, 20) (6, 21) (7, 10) (7, 11) (7, 13) (7, 16) (7, 17) (7, 19) (7, 20) (8, 9) (8, 10) (8, 12) (8, 13) (8, 14) (8, 15) (8, 17) (8, 18) (8, 20) (8, 21) (9, 10) (9, 11) (9, 12) (9, 13) (9, 14) (9, 15) (9, 19) (9, 20) (9, 21) (10, 12) (10, 14) (10, 15) (10, 16) (10, 17) (10, 18) (10, 19) (10, 21) (11, 12) (11, 13) (11, 14) (11, 15) (11, 17) (11, 18) (11, 19) (11, 20) (12, 13) (12, 14) (12, 15) (12, 16) (12, 17) (12, 18) (12, 20) (12, 21) (13, 14) (13, 16) (13, 18) (13, 19) (13, 20) (13, 21) (14, 16) (14, 17) (14, 18) (14, 19) (14, 20) (14, 21) (15, 16) (15, 17) (15, 18) (15, 19) (15, 20) (15, 21) (16, 17) (16, 18) (16, 19) (16, 20) (16, 21) (17, 18) (17, 19) (17, 20) (17, 21) (18, 19) (18, 20) (18, 21) (19, 20) (19, 21) (20, 21) |
| 44 | (3, 7) (3, 13) (3, 19) (5, 7) (5, 17) (5, 21) (7, 13) (7, 15) (7, 17) (7, 19) (9, 13) (9, 15) (9, 19) (9, 21) (13, 15) (13, 17) (13, 19) (13, 21) (15, 17) (15, 19) (15, 21) (17, 19) (17, 21) (19, 21) |
| 45 | (4, 7) (4, 11) (4, 14) (4, 19) (4, 22) (7, 8) (7, 11) (7, 13) (7, 16) (7, 22) (8, 11) (8, 14) (8, 17) (8, 19) (8, 22) (11, 13) (11, 14) (11, 16) (11, 19) (13, 14) (13, 17) (13, 22) (14, 16) (14, 19) (14, 22) (16, 17) (16, 19) (16, 22) (17, 19) (17, 22) (19, 22) |
| 46 | (3, 5) (3, 11) (3, 17) (5, 7) (5, 9) (5, 13) (5, 17) (5, 19) (7, 9) (7, 15) (7, 17) (7, 19) (9, 11) (9, 13) (9, 15) (9, 17) (9, 21) (11, 15) (11, 17) (11, 19) (11, 21) (13, 15) (13, 17) (13, 19) (13, 21) (15, 17) (15, 19) (15, 21) (17, 19) (17, 21) (19, 21) |
| 47 | (3, 7) (3, 10) (3, 13) (3, 16) (3, 19) (4, 5) (4, 6) (4, 9) (4, 10) (4, 13) (4, 14) (4, 17) (4, 18) (4, 21) (4, 22) (5, 8) (5, 9) (5, 11) (5, 13) (5, 16) (5, 18) (5, 19) (5, 23) (6, 7) (6, 8) (6, 9) (6, 10) (6, 13) (6, 14) (6, 15) (6, 16) (6, 19) (6, 20) (6, 21) (6, 22) (7, 9) (7, 11) (7, 13) (7, 15) (7, 16) (7, 17) (7, 18) (7, 22) (7, 23) (8, 9) (8, 10) (8, 11) (8, 12) (8, 14) (8, 17) (8, 18) (8, 19) (8, 20) (8, 21) (8, 22) (9, 10) (9, 12) (9, 13) (9, 14) (9, 15) (9, 16) (9, 17) (9, 21) (9, 22) (9, 23) (10, 11) (10, 12) (10, 13) (10, 14) (10, 15) (10, 16) (10, 18) (10, 19) (10, 21) (10, 22) (10, 23) (11, 13) (11, 15) (11, 16) (11, 17) (11, 19) (11, 20) (11, 21) (11, 23) (12, 13) (12, 14) (12, 15) (12, 16) (12, 17) (12, 18) (12, 19) (12, 20) (12, 21) (12, 22) (13, 14) (13, 15) (13, 16) (13, 18) (13, 19) (13, 20) (13, 22) (13, 23) (14, 15) (14, 16) (14, 17) (14, 18) (14, 20) (14, 21) (14, 22) (14, 23) (15, 18) (15, 19) (15, 20) (15, 21) (15, 22) (15, 23) (16, 17) (16, 18) (16, 19) (16, 20) (16, 21) (16, 22) (16, 23) (17, 18) (17, 19) (17, 20) (17, 21) (17, 22) (17, 23) (18, 19) (18, 20) (18, 21) (18, 22) (18, 23) (19, 20) (19, 21) (19, 22) (19, 23) (20, 21) (20, 22) (20, 23) (21, 22) (21, 23) (22, 23) |
| 48 | (5, 7) (5, 11) (5, 17) (5, 19) (7, 11) (7, 17) (7, 19) (7, 23) (11, 13) (11, 17) (11, 19) (11, 23) (13, 17) (13, 19) (13, 23) (17, 19) (17, 23) (19, 23) |
| 49 | (3, 5) (3, 8) (3, 11) (3, 17) (3, 20) (4, 6) (4, 10) (4, 11) (4, 18) (4, 19) (4, 22) (4, 23) (5, 6) (5, 8) (5, 12) (5, 13) (5, 16) (5, 17) (5, 18) (5, 23) (6, 8) (6, 9) (6, 10) (6, 11) (6, 15) (6, 16) (6, 17) (6, 20) (6, 22) (6, 23) (8, 10) (8, 11) (8, 12) (8, 13) (8, 15) (8, 18) (8, 19) (8, 20) (8, 22) (8, 23) (9, 11) (9, 12) (9, 15) (9, 16) (9, 17) (9, 19) (9, 23) (9, 24) (10, 11) (10, 12) (10, 15) (10, 16) (10, 17) (10, 18) (10, 22) (10, 23) (10, 24) (11, 12) (11, 13) (11, 15) (11, 17) (11, 18) (11, 20) (11, 23) (11, 24) (12, 15) (12, 16) (12, 17) (12, 18) (12, 19) (12, 20) (12, 22) (12, 23) (13, 15) (13, 16) (13, 17) (13, 19) (13, 20) (13, 22) (13, 24) (15, 16) (15, 18) (15, 20) (15, 22) (15, 23) (15, 24) (16, 18) (16, 19) (16, 20) (16, 22) (16, 23) (16, 24) (17, 18) (17, 19) (17, 20) (17, 22) (17, 23) (17, 24) (18, 19) (18, 20) (18, 22) (18, 23) (18, 24) (19, 20) (19, 22) (19, 23) (19, 24) (20, 22) (20, 23) (20, 24) (22, 23) (22, 24) (23, 24) |
| 50 | (3, 7) (3, 13) (3, 19) (7, 9) (7, 11) (7, 13) (7, 17) (7, 19) (7, 23) (9, 11) (9, 13) (9, 17) (9, 19) (9, 21) (11, 19) (11, 21) (11, 23) (13, 17) (13, 19) (13, 21) (13, 23) (17, 19) (17, 21) (17, 23) (19, 21) (19, 23) (21, 23) |
| 51 | (4, 5) (4, 10) (4, 13) (4, 14) (4, 22) (4, 25) (5, 7) (5, 8) (5, 13) (5, 14) (5, 19) (5, 22) (7, 8) (7, 10) (7, 13) (7, 19) (7, 20) (7, 25) (8, 10) (8, 13) (8, 14) (8, 20) (8, 22) (8, 23) (8, 25) (10, 13) (10, 14) (10, 16) (10, 19) (10, 22) (10, 23) (10, 25) (11, 13) (11, 14) (11, 16) (11, 19) (11, 23) (11, 25) (13, 14) (13, 16) (13, 20) (13, 22) (13, 23) (14, 16) (14, 19) (14, 20) (14, 22) (14, 25) (16, 20) (16, 22) (16, 23) (16, 25) (19, 20) (19, 22) (19, 23) (19, 25) (20, 22) (20, 23) (20, 25) (22, 23) (22, 25) (23, 25) |
| 52 | (3, 5) (3, 11) (3, 17) (3, 23) (5, 9) (5, 11) (5, 19) (5, 21) (5, 23) (7, 11) (7, 19) (7, 23) (7, 25) (9, 11) (9, 15) (9, 17) (9, 19) (9, 21) (9, 23) (11, 15) (11, 17) (11, 21) (11, 23) (11, 25) (15, 17) (15, 19) (15, 21) (15, 23) (15, 25) (17, 19) (17, 21) (17, 23) (17, 25) (19, 21) (19, 23) (19, 25) (21, 23) (21, 25) (23, 25) |
| 53 | (3, 4) (3, 7) (3, 13) (3, 16) (3, 19) (3, 22) (4, 6) (4, 10) (4, 11) (4, 14) (4, 15) (4, 18) (4, 19) (4, 22) (4, 23) (4, 26) (5, 7) (5, 9) (5, 11) (5, 14) (5, 17) (5, 19) (5, 21) (5, 22) (5, 26) (6, 7) (6, 8) (6, 9) (6, 10) (6, 13) (6, 14) (6, 15) (6, 16) (6, 19) (6, 20) (6, 21) (6, 22) (6, 25) (6, 26) (7, 8) (7, 9) (7, 10) (7, 12) (7, 13) (7, 15) (7, 16) (7, 17) (7, 19) (7, 20) (7, 22) (7, 24) (7, 26) (8, 10) (8, 11) (8, 12) (8, 14) (8, 17) (8, 18) (8, 19) (8, 20) (8, 22) (8, 23) (8, 25) (8, 26) (9, 10) (9, 12) (9, 13) (9, 14) (9, 15) (9, 16) (9, 19) (9, 20) (9, 21) (9, 23) (9, 24) (9, 25) (10, 11) (10, 12) (10, 14) (10, 15) (10, 16) (10, 17) (10, 18) (10, 19) (10, 21) (10, 22) (10, 24) (10, 25) (10, 26) (11, 12) (11, 13) (11, 15) (11, 16) (11, 17) (11, 18) (11, 19) (11, 23) (11, 24) (11, 25) (11, 26) (12, 13) (12, 14) (12, 15) (12, 16) (12, 18) (12, 19) (12, 20) (12, 21) (12, 22) (12, 23) (12, 25) (12, 26) (13, 15) (13, 16) (13, 17) (13, 18) (13, 19) (13, 21) (13, 22) (13, 23) (13, 24) (13, 25) (14, 15) (14, 16) (14, 17) (14, 18) (14, 19) (14, 20) (14, 21) (14, 22) (14, 23) (14, 24) (14, 26) (15, 16) (15, 17) (15, 18) (15, 20) (15, 21) (15, 22) (15, 24) (15, 25) (15, 26) (16, 17) (16, 18) (16, 19) (16, 20) (16, 22) (16, 23) (16, 24) (16, 25) (16, 26) (17, 20) (17, 21) (17, 22) (17, 23) (17, 24) (17, 25) (17, 26) (18, 19) (18, 20) (18, 21) (18, 22) (18, 23) (18, 24) (18, 25) (18, 26) (19, 20) (19, 21) (19, 22) (19, 23) (19, 24) (19, 25) (19, 26) (20, 21) (20, 22) (20, 23) (20, 24) (20, 25) (20, 26) (21, 22) (21, 23) (21, 24) (21, 25) (21, 26) (22, 23) (22, 24) (22, 25) (22, 26) (23, 24) (23, 25) (23, 26) (24, 25) (24, 26) (25, 26) |
| 54 | (5, 11) (5, 13) (5, 17) (5, 23) (7, 11) (7, 13) (7, 17) (7, 23) (7, 25) (11, 13) (11, 17) (11, 19) (11, 23) (11, 25) (13, 17) (13, 19) (13, 23) (13, 25) (17, 19) (17, 23) (17, 25) (19, 23) (19, 25) (23, 25) |
| 55 | (3, 8) (3, 14) (3, 17) (3, 23) (4, 6) (4, 9) (4, 13) (4, 14) (4, 18) (4, 21) (4, 26) (6, 8) (6, 9) (6, 14) (6, 16) (6, 17) (6, 21) (6, 23) (6, 26) (6, 27) (7, 9) (7, 17) (7, 18) (7, 19) (7, 23) (7, 26) (8, 9) (8, 12) (8, 13) (8, 14) (8, 17) (8, 18) (8, 19) (8, 21) (8, 26) (8, 27) (9, 12) (9, 13) (9, 14) (9, 16) (9, 17) (9, 21) (9, 24) (9, 26) (12, 13) (12, 14) (12, 16) (12, 17) (12, 18) (12, 21) (12, 23) (12, 26) (12, 27) (13, 17) (13, 18) (13, 19) (13, 23) (13, 24) (13, 27) (14, 16) (14, 17) (14, 18) (14, 19) (14, 21) (14, 23) (14, 24) (14, 26) (16, 17) (16, 18) (16, 19) (16, 21) (16, 24) (16, 26) (16, 27) (17, 18) (17, 23) (17, 24) (17, 26) (17, 27) (18, 21) (18, 23) (18, 24) (18, 26) (18, 27) (19, 21) (19, 23) (19, 24) (19, 26) (19, 27) (21, 23) (21, 24) (21, 26) (21, 27) (23, 24) (23, 26) (23, 27) (24, 26) (24, 27) (26, 27) |
| 56 | (3, 13) (3, 19) (3, 25) (5, 9) (5, 13) (5, 19) (5, 23) (5, 27) (9, 13) (9, 15) (9, 17) (9, 19) (9, 23) (9, 25) (11, 13) (11, 17) (11, 19) (11, 25) (11, 27) (13, 15) (13, 19) (13, 23) (13, 25) (13, 27) (15, 17) (15, 19) (15, 23) (15, 25) (15, 27) (17, 19) (17, 23) (17, 25) (17, 27) (19, 23) (19, 25) (19, 27) (23, 25) (23, 27) (25, 27) |
| 57 | (4, 7) (4, 10) (4, 11) (4, 14) (4, 22) (4, 23) (4, 26) (5, 8) (5, 11) (5, 14) (5, 16) (5, 23) (5, 28) (7, 11) (7, 13) (7, 16) (7, 17) (7, 20) (7, 23) (7, 26) (8, 10) (8, 11) (8, 13) (8, 14) (8, 20) (8, 22) (8, 23) (8, 26) (8, 28) (10, 11) (10, 13) (10, 14) (10, 16) (10, 22) (10, 23) (10, 25) (10, 26) (10, 28) (11, 14) (11, 16) (11, 17) (11, 20) (11, 25) (11, 26) (11, 28) (13, 14) (13, 16) (13, 17) (13, 20) (13, 23) (13, 25) (13, 28) (14, 16) (14, 17) (14, 20) (14, 22) (14, 23) (14, 25) (14, 26) (16, 17) (16, 20) (16, 22) (16, 23) (16, 26) (16, 28) (17, 22) (17, 25) (17, 26) (17, 28) (20, 22) (20, 23) (20, 25) (20, 26) (20, 28) (22, 23) (22, 25) (22, 26) (22, 28) (23, 25) (23, 26) (23, 28) (25, 26) (25, 28) (26, 28) |
| 58 | (3, 17) (3, 23) (5, 7) (5, 9) (5, 11) (5, 17) (5, 19) (5, 21) (5, 27) (7, 11) (7, 13) (7, 15) (7, 19) (7, 25) (7, 27) (9, 11) (9, 15) (9, 17) (9, 19) (9, 21) (9, 23) (9, 25) (11, 13) (11, 15) (11, 17) (11, 19) (11, 21) (11, 23) (11, 27) (13, 17) (13, 21) (13, 23) (13, 25) (13, 27) (15, 17) (15, 19) (15, 21) (15, 23) (15, 25) (15, 27) (17, 19) (17, 21) (17, 23) (17, 25) (17, 27) (19, 21) (19, 23) (19, 25) (19, 27) (21, 23) (21, 25) (21, 27) (23, 25) (23, 27) (25, 27) |
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| 60 | (7, 13) (7, 17) (7, 19) (7, 23) (7, 29) (11, 13) (11, 17) (11, 19) (11, 23) (11, 29) (13, 17) (13, 19) (13, 23) (13, 29) (17, 19) (17, 23) (17, 29) (19, 23) (19, 29) (23, 29) |
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| 62 | (3, 7) (3, 13) (3, 19) (3, 25) (5, 9) (5, 11) (5, 13) (5, 21) (5, 23) (5, 29) (7, 9) (7, 15) (7, 17) (7, 19) (7, 23) (7, 25) (7, 29) (9, 11) (9, 13) (9, 15) (9, 19) (9, 21) (9, 23) (9, 25) (9, 29) (11, 13) (11, 15) (11, 19) (11, 21) (11, 23) (11, 25) (11, 27) (13, 15) (13, 17) (13, 19) (13, 21) (13, 25) (13, 27) (13, 29) (15, 19) (15, 21) (15, 23) (15, 25) (15, 27) (15, 29) (17, 19) (17, 21) (17, 23) (17, 25) (17, 27) (17, 29) (19, 21) (19, 23) (19, 25) (19, 27) (19, 29) (21, 23) (21, 25) (21, 27) (21, 29) (23, 25) (23, 27) (23, 29) (25, 27) (25, 29) (27, 29) |
| 63 | (4, 5) (4, 10) (4, 13) (4, 17) (4, 22) (4, 25) (4, 26) (4, 29) (5, 11) (5, 16) (5, 17) (5, 19) (5, 22) (5, 26) (5, 31) (8, 10) (8, 13) (8, 17) (8, 19) (8, 20) (8, 22) (8, 25) (8, 26) (8, 29) (10, 11) (10, 16) (10, 17) (10, 19) (10, 22) (10, 25) (10, 26) (10, 29) (10, 31) (11, 16) (11, 17) (11, 20) (11, 23) (11, 25) (11, 29) (11, 31) (13, 16) (13, 17) (13, 19) (13, 20) (13, 22) (13, 23) (13, 29) (13, 31) (16, 17) (16, 19) (16, 20) (16, 22) (16, 23) (16, 25) (16, 26) (16, 29) (17, 19) (17, 20) (17, 22) (17, 25) (17, 26) (17, 31) (19, 20) (19, 23) (19, 26) (19, 29) (19, 31) (20, 22) (20, 25) (20, 26) (20, 29) (20, 31) (22, 23) (22, 25) (22, 26) (22, 29) (22, 31) (23, 25) (23, 26) (23, 29) (23, 31) (25, 26) (25, 29) (25, 31) (26, 29) (26, 31) (29, 31) |
| 64 | (3, 5) (3, 11) (3, 17) (3, 23) (3, 29) (5, 7) (5, 11) (5, 13) (5, 17) (5, 21) (5, 23) (5, 27) (5, 31) (7, 9) (7, 11) (7, 13) (7, 17) (7, 23) (7, 25) (7, 27) (7, 31) (9, 13) (9, 15) (9, 17) (9, 21) (9, 23) (9, 25) (9, 29) (9, 31) (11, 13) (11, 15) (11, 17) (11, 19) (11, 21) (11, 23) (11, 25) (11, 27) (11, 29) (13, 15) (13, 19) (13, 21) (13, 23) (13, 27) (13, 29) (13, 31) (15, 17) (15, 21) (15, 23) (15, 25) (15, 27) (15, 29) (15, 31) (17, 19) (17, 21) (17, 23) (17, 25) (17, 27) (17, 29) (17, 31) (19, 21) (19, 23) (19, 25) (19, 27) (19, 29) (19, 31) (21, 23) (21, 25) (21, 27) (21, 29) (21, 31) (23, 25) (23, 27) (23, 29) (23, 31) (25, 27) (25, 29) (25, 31) (27, 29) (27, 31) (29, 31) |
| 65 | (3, 4) (3, 7) (3, 16) (3, 19) (3, 22) (3, 28) (4, 6) (4, 7) (4, 11) (4, 14) (4, 18) (4, 19) (4, 22) (4, 23) (4, 27) (4, 31) (6, 7) (6, 8) (6, 9) (6, 14) (6, 16) (6, 19) (6, 21) (6, 22) (6, 27) (6, 28) (6, 31) (6, 32) (7, 8) (7, 11) (7, 12) (7, 17) (7, 18) (7, 19) (7, 22) (7, 24) (7, 27) (7, 31) (7, 32) (8, 11) (8, 12) (8, 14) (8, 18) (8, 21) (8, 22) (8, 23) (8, 27) (8, 28) (8, 29) (8, 31) (9, 12) (9, 16) (9, 17) (9, 19) (9, 21) (9, 22) (9, 23) (9, 24) (9, 31) (9, 32) (11, 12) (11, 14) (11, 16) (11, 17) (11, 19) (11, 23) (11, 24) (11, 28) (11, 29) (11, 31) (12, 14) (12, 16) (12, 18) (12, 19) (12, 21) (12, 22) (12, 23) (12, 27) (12, 28) (12, 31) (12, 32) (14, 16) (14, 18) (14, 19) (14, 21) (14, 22) (14, 24) (14, 27) (14, 29) (14, 31) (14, 32) (16, 18) (16, 19) (16, 21) (16, 22) (16, 23) (16, 24) (16, 27) (16, 28) (16, 29) (16, 31) (17, 18) (17, 19) (17, 21) (17, 22) (17, 23) (17, 27) (17, 28) (17, 29) (17, 32) (18, 19) (18, 21) (18, 22) (18, 23) (18, 24) (18, 27) (18, 28) (18, 31) (18, 32) (19, 21) (19, 22) (19, 24) (19, 28) (19, 29) (19, 31) (19, 32) (21, 24) (21, 27) (21, 28) (21, 29) (21, 31) (21, 32) (22, 23) (22, 24) (22, 27) (22, 28) (22, 29) (22, 31) (22, 32) (23, 24) (23, 27) (23, 28) (23, 29) (23, 31) (23, 32) (24, 27) (24, 28) (24, 29) (24, 31) (24, 32) (27, 28) (27, 29) (27, 31) (27, 32) (28, 29) (28, 31) (28, 32) (29, 31) (29, 32) (31, 32) |
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38) (25, 39) (25, 40) (25, 41) (25, 42) (25, 43) (25, 44) (25, 45) (25, 46) (25, 48) (26, 27) (26, 28) (26, 29) (26, 30) (26, 31) (26, 32) (26, 33) (26, 34) (26, 35) (26, 36) (26, 37) (26, 38) (26, 39) (26, 40) (26, 41) (26, 42) (26, 43) (26, 44) (26, 46) (26, 47) (26, 48) (27, 28) (27, 29) (27, 30) (27, 31) (27, 32) (27, 33) (27, 34) (27, 36) (27, 37) (27, 38) (27, 39) (27, 40) (27, 41) (27, 42) (27, 44) (27, 45) (27, 46) (27, 47) (27, 48) (28, 29) (28, 30) (28, 31) (28, 32) (28, 33) (28, 34) (28, 35) (28, 36) (28, 37) (28, 38) (28, 39) (28, 40) (28, 42) (28, 43) (28, 44) (28, 45) (28, 46) (28, 47) (28, 48) (29, 30) (29, 31) (29, 32) (29, 33) (29, 35) (29, 36) (29, 37) (29, 38) (29, 40) (29, 41) (29, 42) (29, 43) (29, 44) (29, 45) (29, 46) (29, 47) (29, 48) (30, 31) (30, 32) (30, 33) (30, 34) (30, 35) (30, 36) (30, 38) (30, 39) (30, 40) (30, 41) (30, 42) (30, 43) (30, 44) (30, 45) (30, 46) (30, 47) (30, 48) (31, 32) (31, 34) (31, 36) (31, 37) (31, 38) (31, 39) (31, 40) (31, 41) (31, 42) (31, 43) (31, 44) (31, 45) (31, 46) (31, 47) (31, 48) (32, 34) (32, 35) (32, 36) (32, 37) (32, 38) (32, 39) (32, 40) (32, 41) (32, 42) (32, 43) (32, 44) (32, 45) (32, 46) (32, 47) (32, 48) (33, 34) (33, 35) (33, 36) (33, 37) (33, 38) (33, 39) (33, 40) (33, 41) (33, 42) (33, 43) (33, 44) (33, 45) (33, 46) (33, 47) (33, 48) (34, 35) (34, 36) (34, 37) (34, 38) (34, 39) (34, 40) (34, 41) (34, 42) (34, 43) (34, 44) (34, 45) (34, 46) (34, 47) (34, 48) (35, 36) (35, 37) (35, 38) (35, 39) (35, 40) (35, 41) (35, 42) (35, 43) (35, 44) (35, 45) (35, 46) (35, 47) (35, 48) (36, 37) (36, 38) (36, 39) (36, 40) (36, 41) (36, 42) (36, 43) (36, 44) (36, 45) (36, 46) (36, 47) (36, 48) (37, 38) (37, 39) (37, 40) (37, 41) (37, 42) (37, 43) (37, 44) (37, 45) (37, 46) (37, 47) (37, 48) (38, 39) (38, 40) (38, 41) (38, 42) (38, 43) (38, 44) (38, 45) (38, 46) (38, 47) (38, 48) (39, 40) (39, 41) (39, 42) (39, 43) (39, 44) (39, 45) (39, 46) (39, 47) (39, 48) (40, 41) (40, 42) (40, 43) (40, 44) (40, 45) (40, 46) (40, 47) (40, 48) (41, 42) (41, 43) (41, 44) (41, 45) (41, 46) (41, 47) (41, 48) (42, 43) (42, 44) (42, 45) (42, 46) (42, 47) (42, 48) (43, 44) (43, 45) (43, 46) (43, 47) (43, 48) (44, 45) (44, 46) (44, 47) (44, 48) (45, 46) (45, 47) (45, 48) (46, 47) (46, 48) (47, 48) |
| 98 | (3, 13) (3, 25) (3, 31) (3, 37) (3, 43) (5, 9) (5, 11) (5, 17) (5, 19) (5, 27) (5, 29) (5, 37) (5, 39) (5, 41) (5, 47) (9, 11) (9, 13) (9, 15) (9, 19) (9, 23) (9, 25) (9, 29) (9, 31) (9, 33) (9, 37) (9, 39) (9, 41) (9, 43) (9, 47) (11, 13) (11, 15) (11, 17) (11, 19) (11, 23) (11, 25) (11, 27) (11, 31) (11, 37) (11, 39) (11, 41) (11, 45) (11, 47) (13, 15) (13, 19) (13, 23) (13, 25) (13, 27) (13, 29) (13, 31) (13, 37) (13, 41) (13, 43) (13, 45) (13, 47) (15, 17) (15, 19) (15, 25) (15, 27) (15, 29) (15, 31) (15, 33) (15, 37) (15, 39) (15, 41) (15, 43) (15, 47) (17, 19) (17, 23) (17, 25) (17, 29) (17, 31) (17, 33) (17, 37) (17, 39) (17, 41) (17, 43) (17, 45) (19, 23) (19, 25) (19, 27) (19, 29) (19, 31) (19, 33) (19, 37) (19, 39) (19, 43) (19, 45) (19, 47) (23, 27) (23, 31) (23, 33) (23, 37) (23, 39) (23, 41) (23, 43) (23, 45) (23, 47) (25, 27) (25, 29) (25, 31) (25, 33) (25, 37) (25, 39) (25, 41) (25, 43) (25, 45) (25, 47) (27, 29) (27, 31) (27, 33) (27, 37) (27, 39) (27, 41) (27, 43) (27, 45) (27, 47) (29, 31) (29, 33) (29, 37) (29, 39) (29, 41) (29, 43) (29, 45) (29, 47) (31, 33) (31, 37) (31, 39) (31, 41) (31, 43) (31, 45) (31, 47) (33, 37) (33, 39) (33, 41) (33, 43) (33, 45) (33, 47) (37, 39) (37, 41) (37, 43) (37, 45) (37, 47) (39, 41) (39, 43) (39, 45) (39, 47) (41, 43) (41, 45) (41, 47) (43, 45) (43, 47) (45, 47) |
| 99 | (4, 10) (4, 13) (4, 14) (4, 17) (4, 25) (4, 26) (4, 29) (4, 34) (4, 37) (4, 38) (4, 41) (4, 46) (4, 49) (5, 7) (5, 8) (5, 13) (5, 16) (5, 17) (5, 23) (5, 26) (5, 28) (5, 31) (5, 32) (5, 37) (5, 38) (5, 41) (5, 43) (5, 46) (7, 10) (7, 13) (7, 16) (7, 17) (7, 19) (7, 20) (7, 25) (7, 26) (7, 31) (7, 32) (7, 34) (7, 37) (7, 38) (7, 40) (7, 41) (7, 47) (8, 10) (8, 14) (8, 17) (8, 20) (8, 23) (8, 25) (8, 26) (8, 28) (8, 29) (8, 31) (8, 34) (8, 37) (8, 38) (8, 41) (8, 46) (8, 47) (8, 49) (10, 13) (10, 14) (10, 16) (10, 17) (10, 23) (10, 25) (10, 26) (10, 28) (10, 31) (10, 32) (10, 34) (10, 35) (10, 37) (10, 38) (10, 41) (10, 43) (10, 46) (10, 47) (13, 14) (13, 16) (13, 17) (13, 19) (13, 20) (13, 23) (13, 25) (13, 28) (13, 29) (13, 31) (13, 32) (13, 35) (13, 37) (13, 38) (13, 40) (13, 41) (13, 46) (13, 49) (14, 16) (14, 19) (14, 20) (14, 23) (14, 25) (14, 26) (14, 31) (14, 32) (14, 34) (14, 35) (14, 37) (14, 38) (14, 40) (14, 41) (14, 46) (14, 47) (14, 49) (16, 17) (16, 20) (16, 23) (16, 25) (16, 26) (16, 28) (16, 29) (16, 31) (16, 34) (16, 37) (16, 38) (16, 40) (16, 41) (16, 43) (16, 46) (16, 47) (16, 49) (17, 19) (17, 20) (17, 23) (17, 25) (17, 26) (17, 28) (17, 29) (17, 32) (17, 35) (17, 37) (17, 38) (17, 40) (17, 43) (17, 46) (17, 47) (17, 49) (19, 25) (19, 26) (19, 28) (19, 29) (19, 31) (19, 32) (19, 34) (19, 35) (19, 37) (19, 41) (19, 43) (19, 46) (19, 47) (19, 49) (20, 23) (20, 25) (20, 26) (20, 28) (20, 29) (20, 31) (20, 32) (20, 34) (20, 35) (20, 37) (20, 38) (20, 41) (20, 43) (20, 46) (20, 47) (20, 49) (23, 25) (23, 26) (23, 28) (23, 29) (23, 31) (23, 32) (23, 34) (23, 35) (23, 37) (23, 40) (23, 41) (23, 43) (23, 47) (23, 49) (25, 26) (25, 28) (25, 29) (25, 31) (25, 32) (25, 34) (25, 35) (25, 38) (25, 40) (25, 41) (25, 43) (25, 46) (25, 47) (26, 28) (26, 29) (26, 31) (26, 32) (26, 34) (26, 35) (26, 37) (26, 38) (26, 40) (26, 41) (26, 43) (26, 46) (26, 49) (28, 29) (28, 31) (28, 32) (28, 34) (28, 35) (28, 37) (28, 38) (28, 40) (28, 41) (28, 46) (28, 47) (28, 49) (29, 31) (29, 32) (29, 34) (29, 37) (29, 38) (29, 40) (29, 43) (29, 46) (29, 47) (29, 49) (31, 32) (31, 35) (31, 38) (31, 40) (31, 41) (31, 43) (31, 46) (31, 47) (31, 49) (32, 34) (32, 37) (32, 38) (32, 40) (32, 41) (32, 43) (32, 46) (32, 47) (32, 49) (34, 35) (34, 37) (34, 38) (34, 40) (34, 41) (34, 43) (34, 46) (34, 47) (34, 49) (35, 37) (35, 38) (35, 40) (35, 41) (35, 43) (35, 46) (35, 47) (35, 49) (37, 38) (37, 40) (37, 41) (37, 43) (37, 46) (37, 47) (37, 49) (38, 40) (38, 41) (38, 43) (38, 46) (38, 47) (38, 49) (40, 41) (40, 43) (40, 46) (40, 47) (40, 49) (41, 43) (41, 46) (41, 47) (41, 49) (43, 46) (43, 47) (43, 49) (46, 47) (46, 49) (47, 49) |
| 100 | (3, 11) (3, 17) (3, 23) (3, 29) (3, 41) (3, 47) (7, 11) (7, 13) (7, 17) (7, 19) (7, 27) (7, 29) (7, 33) (7, 39) (7, 41) (7, 43) (7, 47) (9, 11) (9, 17) (9, 21) (9, 23) (9, 29) (9, 31) (9, 33) (9, 39) (9, 41) (9, 43) (9, 47) (9, 49) (11, 13) (11, 17) (11, 19) (11, 21) (11, 27) (11, 29) (11, 31) (11, 37) (11, 39) (11, 41) (11, 43) (11, 47) (11, 49) (13, 17) (13, 19) (13, 21) (13, 23) (13, 27) (13, 31) (13, 33) (13, 37) (13, 41) (13, 43) (13, 47) (13, 49) (17, 19) (17, 21) (17, 23) (17, 27) (17, 29) (17, 31) (17, 33) (17, 37) (17, 39) (17, 41) (17, 43) (17, 47) (19, 21) (19, 23) (19, 29) (19, 31) (19, 33) (19, 37) (19, 39) (19, 41) (19, 47) (19, 49) (21, 23) (21, 27) (21, 29) (21, 31) (21, 33) (21, 39) (21, 41) (21, 43) (21, 47) (21, 49) (23, 27) (23, 29) (23, 33) (23, 37) (23, 39) (23, 41) (23, 43) (23, 47) (23, 49) (27, 29) (27, 31) (27, 33) (27, 37) (27, 39) (27, 41) (27, 43) (27, 47) (27, 49) (29, 31) (29, 33) (29, 37) (29, 39) (29, 41) (29, 43) (29, 47) (29, 49) (31, 33) (31, 37) (31, 39) (31, 41) (31, 43) (31, 47) (31, 49) (33, 37) (33, 39) (33, 41) (33, 43) (33, 47) (33, 49) (37, 39) (37, 41) (37, 43) (37, 47) (37, 49) (39, 41) (39, 43) (39, 47) (39, 49) (41, 43) (41, 47) (41, 49) (43, 47) (43, 49) (47, 49) |
Trivia
- 11 is the smallest EDO with an independent pair of generators
- 15 is the largest EDO without one (probably)
- EDOs with more independent pairs than any smaller one: 11 (1), 13 (2), 17 (7), 19 (10), 23 (19), 29 (39), 31 (47), 37 (76), 41 (101)
- The same, but counting only composite EDOs: 16 (2), 22 (3), 25 (13), 33 (15), 35 (23), 39 (27), 45 (31), 49 (113), 65 (160), 77 (271), 85 (323), 91 (422), 95 (429)