Minimum monotone vals
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.