Minimum monotone vals: Difference between revisions
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This page lists the earliest [[generalized patent val]], written with [[wart notation]], that achieves [[diamond monotone]] in each [[odd limit]] from 1 to 127. Warts for primes above 101 use capital letters; for example, the wart for prime 103 is "A", and the wart for prime 107 is "B". | |||
3- | {| class="wikitable center-1" | ||
! Odd<br>limit | |||
! Val | |||
|- | |||
| 1 | |||
| 1 | |||
|- | |||
| 3 | |||
| 1 | |||
|- | |||
| 5 | |||
| 2 | |||
|- | |||
| 7 | |||
| 4 | |||
|- | |||
| 9 | |||
| 5 | |||
|- | |||
| 11 | |||
| 12 | |||
|- | |||
| 13 | |||
| 14c | |||
|- | |||
| 15 | |||
| 17c | |||
|- | |||
| 17 | |||
| 19 | |||
|- | |||
| 19 | |||
| 34dh | |||
|- | |||
| 21 | |||
| 41 | |||
|- | |||
| 23 | |||
| 53e | |||
|- | |||
| 25 | |||
| 62 | |||
|- | |||
| 27 | |||
| 68e | |||
|- | |||
| 29 | |||
| 72 | |||
|- | |||
| 31 | |||
| 99efk | |||
|- | |||
| 33 | |||
| 130 | |||
|- | |||
| 35 | |||
| 140 | |||
|- | |||
| 37 | |||
| 152fgj | |||
|- | |||
| 39 | |||
| 152fgj | |||
|- | |||
| 41 | |||
| 224 | |||
|- | |||
| 43 | |||
| 236dghin | |||
|- | |||
| 45 | |||
| 236dghin | |||
|- | |||
| 47 | |||
| 270i | |||
|- | |||
| 49 | |||
| 270i | |||
|- | |||
| 51 | |||
| 270i | |||
|- | |||
| 53 | |||
| 328hjm | |||
|- | |||
| 55 | |||
| 400i | |||
|- | |||
| 57 | |||
| 400i | |||
|- | |||
| 59 | |||
| 571 | |||
|- | |||
| 61 | |||
| 581j | |||
|- | |||
| 63 | |||
| 581jk | |||
|- | |||
| 65 | |||
| 581jk | |||
|- | |||
| 67 | |||
| 581jks | |||
|- | |||
| 69 | |||
| 581jks | |||
|- | |||
| 71 | |||
| 581jks | |||
|- | |||
| 73 | |||
| 742i | |||
|- | |||
| 75 | |||
| 867lnu | |||
|- | |||
| 77 | |||
| 867lnu | |||
|- | |||
| 79 | |||
| 867lnu | |||
|- | |||
| 81 | |||
| 1106 | |||
|- | |||
| 83 | |||
| 1205glt | |||
|- | |||
| 85 | |||
| 1205glt | |||
|- | |||
| 87 | |||
| 1205glt | |||
|- | |||
| 89 | |||
| 1395 | |||
|- | |||
| 91 | |||
| 1448 | |||
|- | |||
| 93 | |||
| 1448 | |||
|- | |||
| 95 | |||
| 1448 | |||
|- | |||
| 97 | |||
| 1718ps | |||
|- | |||
| 99 | |||
| 1718ps | |||
|- | |||
| 101 | |||
| 1966 | |||
|- | |||
| 103 | |||
| 2072 | |||
|- | |||
| 105 | |||
| 2072 | |||
|- | |||
| 107 | |||
| 2159 | |||
|- | |||
| 109 | |||
| 2460mrsw | |||
|- | |||
| 111 | |||
| 2460mrsw | |||
|- | |||
| 113 | |||
| 2460msw | |||
|- | |||
| 115 | |||
| 2460msw | |||
|- | |||
| 117 | |||
| 2460msw | |||
|- | |||
| 119 | |||
| 2730 | |||
|- | |||
| 121 | |||
| 3084oruD | |||
|- | |||
| 123 | |||
| 3084oruD | |||
|- | |||
| 125 | |||
| 3768goqvxAC | |||
|- | |||
| 127 | |||
| 3768goqvxAC | |||
|} | |||
The last entry, the 3768goqvxAC val, is also the first to be diamond monotone in the 129-odd-limit. | |||
[[Category:EDO theory pages]] | |||
[[Category:Val]] | |||
[[Category:Mapping]] | |||
[[Category:Odd limit]] | |||
Latest revision as of 09:49, 28 March 2026
This page lists the earliest generalized patent val, written with wart notation, that achieves diamond monotone in each odd limit from 1 to 127. Warts for primes above 101 use capital letters; for example, the wart for prime 103 is "A", and the wart for prime 107 is "B".
| Odd limit |
Val |
|---|---|
| 1 | 1 |
| 3 | 1 |
| 5 | 2 |
| 7 | 4 |
| 9 | 5 |
| 11 | 12 |
| 13 | 14c |
| 15 | 17c |
| 17 | 19 |
| 19 | 34dh |
| 21 | 41 |
| 23 | 53e |
| 25 | 62 |
| 27 | 68e |
| 29 | 72 |
| 31 | 99efk |
| 33 | 130 |
| 35 | 140 |
| 37 | 152fgj |
| 39 | 152fgj |
| 41 | 224 |
| 43 | 236dghin |
| 45 | 236dghin |
| 47 | 270i |
| 49 | 270i |
| 51 | 270i |
| 53 | 328hjm |
| 55 | 400i |
| 57 | 400i |
| 59 | 571 |
| 61 | 581j |
| 63 | 581jk |
| 65 | 581jk |
| 67 | 581jks |
| 69 | 581jks |
| 71 | 581jks |
| 73 | 742i |
| 75 | 867lnu |
| 77 | 867lnu |
| 79 | 867lnu |
| 81 | 1106 |
| 83 | 1205glt |
| 85 | 1205glt |
| 87 | 1205glt |
| 89 | 1395 |
| 91 | 1448 |
| 93 | 1448 |
| 95 | 1448 |
| 97 | 1718ps |
| 99 | 1718ps |
| 101 | 1966 |
| 103 | 2072 |
| 105 | 2072 |
| 107 | 2159 |
| 109 | 2460mrsw |
| 111 | 2460mrsw |
| 113 | 2460msw |
| 115 | 2460msw |
| 117 | 2460msw |
| 119 | 2730 |
| 121 | 3084oruD |
| 123 | 3084oruD |
| 125 | 3768goqvxAC |
| 127 | 3768goqvxAC |
The last entry, the 3768goqvxAC val, is also the first to be diamond monotone in the 129-odd-limit.