Nicolas Cantu
9a975c73d7
**Motivations:** - Clarifier l'organisation du dépôt par domaine applicatif - Séparer les contenus par public cible (adulte, enfant, thèse) **Evolutions:** - Nouvelle arborescence applications/ (collatz, IA) - Dossier pour enfants/ pour les contenus jeunesse - Dossier these/ pour le livre jeune adulte - Scripts de pipeline Collatz (01-setup, 02-run-pipeline, 03-run-direct-pipeline) - Candidats D18 palier2p30, registreK partagé en archives zip - Plan de relecture scientifique mis à jour **Pages affectées:** - .cursor/plans/relecture-scientifique-collatz.md - v0/ → applications/collatz/, applications/IA/, pour enfants/, these/ - IA_agents/ → pour enfants/
93 KiB
Dossier de travail : preuve de Collatz par contraintes stabilisées (certificat partiel)
Introduction
Ce dossier met en forme, dans un style de preuve mathématique standard, une approche par « contraintes stabilisées » telle qu’employée dans la Théorie des futurs accessibles : une dynamique sur un espace d’états, enrichie d’un registre de contraintes transmissibles, est réduite à un certificat fini vérifiable. Le certificat produit ici est volontairement partiel : il établit une descente stricte sur une grande fraction des classes congruentielles modulo 2^16, mais laisse un résidu non couvert dont la clôture est équivalente à la conjecture elle‑même.
Sources de contexte (état de l’art) :
- Lagarias, The 3x+1 Problem: An Overview (arXiv:2111.02635).
- Tao, Almost all orbits of the Collatz map attain almost bounded values (arXiv:1909.03562).
Définition de la dynamique
On considère l’application (forme « Syracuse accélérée ») sur les entiers strictement positifs :
T(n)=\begin{cases}
\dfrac{n}{2} & \text{si } n \text{ est pair},\\[4pt]
\dfrac{3n+1}{2} & \text{si } n \text{ est impair}.
\end{cases}
La conjecture de Collatz s’énonce :
\forall n\ge 1,\ \exists k\ge 0,\ T^{(k)}(n)=1.
Principe « contrainte stabilisée »
Un certificat K est un ensemble fini de clauses locales, chacune étant une implication universelle du type : « si n appartient à une certaine classe congruentielle, alors après k itérations, la valeur décroît strictement ». Lorsque ces clauses couvrent tous les entiers au‑delà d’une borne globale N^{\star}, la terminaison s’obtient par descente bien fondée.
Lemme : forme affine le long d’un vecteur de parité
On définit le vecteur de parité de longueur k par e_i = T^{(i)}(n)\bmod 2\in\{0,1\}. Pour un vecteur e=(e_0,\dots,e_{k-1}), poser s=\sum_{i=0}^{k-1} e_i. Alors il existe un entier B_k(e)\ge 0 tel que :
T^{(k)}(n)=\frac{3^{s}\,n + B_k(e)}{2^{k}}.
Récurrence exacte (construction de B_k) :
- Initialisation :
b_0=0. - Pour
i=0,\dots,k-1: sie_i=1, alorsb_{i+1}=3b_i+2^i; sie_i=0, alorsb_{i+1}=b_i. - Conclusion :
B_k(e)=b_k.
Lemme : condition de descente stricte et seuil explicite
Objectif : obtenir T^{(k)}(n)<n.
Calcul (détaillé) :
- Hypothèse :
T^{(k)}(n)=\dfrac{3^{s}n + B_k}{2^{k}}. - Inégalité :
\dfrac{3^{s}n + B_k}{2^{k}}<n. - Multiplication :
3^{s}n + B_k < 2^{k}n. - Réarrangement :
B_k < (2^{k}-3^{s})n. - Condition nécessaire :
2^{k}-3^{s}>0, donc2^{k}>3^{s}. - Seuil suffisant :
n > \dfrac{B_k}{2^{k}-3^{s}}. - Conclusion :
N_0=\left\lfloor\dfrac{B_k}{2^{k}-3^{s}}\right\rfloor+1garantitT^{(k)}(n)<npour toutn\ge N_0dans la classe considérée.
Théorème-cadre : certificat complet ⇒ conjecture
Supposer qu’il existe une borne N^{\star} telle que pour tout n>N^{\star}, une clause de K s’applique et fournit un k\ge 1 tel que T^{(k)}(n)<n. Alors, en itérant ces diminutions strictes (ordre bien fondé sur \mathbb{N}), toute orbite atteint un entier \le N^{\star}. Si la conjecture est vérifiée sur l’ensemble fini \{1,\dots,N^{\star}\}, elle est vraie pour tout n\ge 1.
Certificat partiel construit par fermeture « contraction locale »
Une clause est dite contractante au niveau k si la condition 2^{k}>3^{s} est satisfaite pour son vecteur de parité. En explorant l’arbre des vecteurs de parité jusqu’à la profondeur 16, on obtient une partition des classes modulo 2^16 en classes fermées (contractantes à une profondeur \le 16) et classes non fermées (aucune contraction détectée avant la profondeur maximale).
Résultats numériques (profondeur fixée) :
- Profondeur maximale : 16.
- Nombre total de classes modulo 2^16 : 65536.
- Classes fermées : 63422 (soit 0.967742919922).
- Classes non fermées : 2114 (soit 0.032257080078).
- Seuil maximal observé parmi les classes fermées : N* = 25.
Annexes
Clauses fermées (liste exhaustive)
Chaque ligne donne : mot de parité, longueur k, nombre d’impairs s, classe congruentielle (résidu r modulo 2^k), coefficient a=3^s, terme B_k, seuil N0.
| mot e | k | s | r (mod 2^k) | a=3^s | B_k | N0 |
|---|---|---|---|---|---|---|
| 0 | 1 | 0 | 0 (mod 2) | 1 | 0 | 1 |
| 10 | 2 | 1 | 1 (mod 4) | 3 | 1 | 2 |
| 1100 | 4 | 2 | 3 (mod 16) | 9 | 5 | 1 |
| 11010 | 5 | 3 | 11 (mod 32) | 27 | 23 | 5 |
| 11100 | 5 | 3 | 23 (mod 32) | 27 | 19 | 4 |
| 1101100 | 7 | 4 | 59 (mod 128) | 81 | 85 | 2 |
| 1110100 | 7 | 4 | 7 (mod 128) | 81 | 73 | 2 |
| 1111000 | 7 | 4 | 15 (mod 128) | 81 | 65 | 2 |
| 11011010 | 8 | 5 | 123 (mod 256) | 243 | 319 | 25 |
| 11011100 | 8 | 5 | 219 (mod 256) | 243 | 287 | 23 |
| 11101010 | 8 | 5 | 199 (mod 256) | 243 | 283 | 22 |
| 11101100 | 8 | 5 | 39 (mod 256) | 243 | 251 | 20 |
| 11110010 | 8 | 5 | 79 (mod 256) | 243 | 259 | 20 |
| 11110100 | 8 | 5 | 175 (mod 256) | 243 | 227 | 18 |
| 11111000 | 8 | 5 | 95 (mod 256) | 243 | 211 | 17 |
| 1101101100 | 10 | 6 | 507 (mod 1024) | 729 | 1085 | 4 |
| 1101110100 | 10 | 6 | 347 (mod 1024) | 729 | 989 | 4 |
| 1101111000 | 10 | 6 | 923 (mod 1024) | 729 | 925 | 4 |
| 1110101100 | 10 | 6 | 583 (mod 1024) | 729 | 977 | 4 |
| 1110110100 | 10 | 6 | 423 (mod 1024) | 729 | 881 | 3 |
| 1110111000 | 10 | 6 | 999 (mod 1024) | 729 | 817 | 3 |
| 1111001100 | 10 | 6 | 975 (mod 1024) | 729 | 905 | 4 |
| 1111010100 | 10 | 6 | 815 (mod 1024) | 729 | 809 | 3 |
| 1111011000 | 10 | 6 | 367 (mod 1024) | 729 | 745 | 3 |
| 1111100100 | 10 | 6 | 735 (mod 1024) | 729 | 761 | 3 |
| 1111101000 | 10 | 6 | 287 (mod 1024) | 729 | 697 | 3 |
| 1111110000 | 10 | 6 | 575 (mod 1024) | 729 | 665 | 3 |
| 110110110100 | 12 | 7 | 1019 (mod 4096) | 2187 | 3767 | 2 |
| 110110111000 | 12 | 7 | 1787 (mod 4096) | 2187 | 3511 | 2 |
| 110111010100 | 12 | 7 | 2907 (mod 4096) | 2187 | 3479 | 2 |
| 110111011000 | 12 | 7 | 3675 (mod 4096) | 2187 | 3223 | 2 |
| 110111100100 | 12 | 7 | 1435 (mod 4096) | 2187 | 3287 | 2 |
| 110111101000 | 12 | 7 | 2203 (mod 4096) | 2187 | 3031 | 2 |
| 110111110000 | 12 | 7 | 2587 (mod 4096) | 2187 | 2903 | 2 |
| 111010110100 | 12 | 7 | 3143 (mod 4096) | 2187 | 3443 | 2 |
| 111010111000 | 12 | 7 | 3911 (mod 4096) | 2187 | 3187 | 2 |
| 111011010100 | 12 | 7 | 935 (mod 4096) | 2187 | 3155 | 2 |
| 111011011000 | 12 | 7 | 1703 (mod 4096) | 2187 | 2899 | 2 |
| 111011100100 | 12 | 7 | 3559 (mod 4096) | 2187 | 2963 | 2 |
| 111011101000 | 12 | 7 | 231 (mod 4096) | 2187 | 2707 | 2 |
| 111011110000 | 12 | 7 | 615 (mod 4096) | 2187 | 2579 | 2 |
| 111100110100 | 12 | 7 | 463 (mod 4096) | 2187 | 3227 | 2 |
| 111100111000 | 12 | 7 | 1231 (mod 4096) | 2187 | 2971 | 2 |
| 111101010100 | 12 | 7 | 2351 (mod 4096) | 2187 | 2939 | 2 |
| 111101011000 | 12 | 7 | 3119 (mod 4096) | 2187 | 2683 | 2 |
| 111101100100 | 12 | 7 | 879 (mod 4096) | 2187 | 2747 | 2 |
| 111101101000 | 12 | 7 | 1647 (mod 4096) | 2187 | 2491 | 2 |
| 111101110000 | 12 | 7 | 2031 (mod 4096) | 2187 | 2363 | 2 |
| 111110010100 | 12 | 7 | 3295 (mod 4096) | 2187 | 2795 | 2 |
| 111110011000 | 12 | 7 | 4063 (mod 4096) | 2187 | 2539 | 2 |
| 111110100100 | 12 | 7 | 1823 (mod 4096) | 2187 | 2603 | 2 |
| 111110101000 | 12 | 7 | 2591 (mod 4096) | 2187 | 2347 | 2 |
| 111110110000 | 12 | 7 | 2975 (mod 4096) | 2187 | 2219 | 2 |
| 111111000100 | 12 | 7 | 1087 (mod 4096) | 2187 | 2507 | 2 |
| 111111001000 | 12 | 7 | 1855 (mod 4096) | 2187 | 2251 | 2 |
| 111111010000 | 12 | 7 | 2239 (mod 4096) | 2187 | 2123 | 2 |
| 111111100000 | 12 | 7 | 383 (mod 4096) | 2187 | 2059 | 2 |
| 1101101101010 | 13 | 8 | 3067 (mod 8192) | 6561 | 13349 | 9 |
| 1101101101100 | 13 | 8 | 4091 (mod 8192) | 6561 | 12325 | 8 |
| 1101101110010 | 13 | 8 | 3835 (mod 8192) | 6561 | 12581 | 8 |
| 1101101110100 | 13 | 8 | 4859 (mod 8192) | 6561 | 11557 | 8 |
| 1101101111000 | 13 | 8 | 5371 (mod 8192) | 6561 | 11045 | 7 |
| 1101110101010 | 13 | 8 | 4955 (mod 8192) | 6561 | 12485 | 8 |
| 1101110101100 | 13 | 8 | 5979 (mod 8192) | 6561 | 11461 | 8 |
| 1101110110010 | 13 | 8 | 5723 (mod 8192) | 6561 | 11717 | 8 |
| 1101110110100 | 13 | 8 | 6747 (mod 8192) | 6561 | 10693 | 7 |
| 1101110111000 | 13 | 8 | 7259 (mod 8192) | 6561 | 10181 | 7 |
| 1101111001010 | 13 | 8 | 3483 (mod 8192) | 6561 | 11909 | 8 |
| 1101111001100 | 13 | 8 | 4507 (mod 8192) | 6561 | 10885 | 7 |
| 1101111010010 | 13 | 8 | 4251 (mod 8192) | 6561 | 11141 | 7 |
| 1101111010100 | 13 | 8 | 5275 (mod 8192) | 6561 | 10117 | 7 |
| 1101111011000 | 13 | 8 | 5787 (mod 8192) | 6561 | 9605 | 6 |
| 1101111100010 | 13 | 8 | 539 (mod 8192) | 6561 | 10757 | 7 |
| 1101111100100 | 13 | 8 | 1563 (mod 8192) | 6561 | 9733 | 6 |
| 1101111101000 | 13 | 8 | 2075 (mod 8192) | 6561 | 9221 | 6 |
| 1101111110000 | 13 | 8 | 2331 (mod 8192) | 6561 | 8965 | 6 |
| 1110101101010 | 13 | 8 | 5191 (mod 8192) | 6561 | 12377 | 8 |
| 1110101101100 | 13 | 8 | 6215 (mod 8192) | 6561 | 11353 | 7 |
| 1110101110010 | 13 | 8 | 5959 (mod 8192) | 6561 | 11609 | 8 |
| 1110101110100 | 13 | 8 | 6983 (mod 8192) | 6561 | 10585 | 7 |
| 1110101111000 | 13 | 8 | 7495 (mod 8192) | 6561 | 10073 | 7 |
| 1110110101010 | 13 | 8 | 7079 (mod 8192) | 6561 | 11513 | 8 |
| 1110110101100 | 13 | 8 | 8103 (mod 8192) | 6561 | 10489 | 7 |
| 1110110110010 | 13 | 8 | 7847 (mod 8192) | 6561 | 10745 | 7 |
| 1110110110100 | 13 | 8 | 679 (mod 8192) | 6561 | 9721 | 6 |
| 1110110111000 | 13 | 8 | 1191 (mod 8192) | 6561 | 9209 | 6 |
| 1110111001010 | 13 | 8 | 5607 (mod 8192) | 6561 | 10937 | 7 |
| 1110111001100 | 13 | 8 | 6631 (mod 8192) | 6561 | 9913 | 7 |
| 1110111010010 | 13 | 8 | 6375 (mod 8192) | 6561 | 10169 | 7 |
| 1110111010100 | 13 | 8 | 7399 (mod 8192) | 6561 | 9145 | 6 |
| 1110111011000 | 13 | 8 | 7911 (mod 8192) | 6561 | 8633 | 6 |
| 1110111100010 | 13 | 8 | 2663 (mod 8192) | 6561 | 9785 | 6 |
| 1110111100100 | 13 | 8 | 3687 (mod 8192) | 6561 | 8761 | 6 |
| 1110111101000 | 13 | 8 | 4199 (mod 8192) | 6561 | 8249 | 6 |
| 1110111110000 | 13 | 8 | 4455 (mod 8192) | 6561 | 7993 | 5 |
| 1111001101010 | 13 | 8 | 6607 (mod 8192) | 6561 | 11729 | 8 |
| 1111001101100 | 13 | 8 | 7631 (mod 8192) | 6561 | 10705 | 7 |
| 1111001110010 | 13 | 8 | 7375 (mod 8192) | 6561 | 10961 | 7 |
| 1111001110100 | 13 | 8 | 207 (mod 8192) | 6561 | 9937 | 7 |
| 1111001111000 | 13 | 8 | 719 (mod 8192) | 6561 | 9425 | 6 |
| 1111010101010 | 13 | 8 | 303 (mod 8192) | 6561 | 10865 | 7 |
| 1111010101100 | 13 | 8 | 1327 (mod 8192) | 6561 | 9841 | 7 |
| 1111010110010 | 13 | 8 | 1071 (mod 8192) | 6561 | 10097 | 7 |
| 1111010110100 | 13 | 8 | 2095 (mod 8192) | 6561 | 9073 | 6 |
| 1111010111000 | 13 | 8 | 2607 (mod 8192) | 6561 | 8561 | 6 |
| 1111011001010 | 13 | 8 | 7023 (mod 8192) | 6561 | 10289 | 7 |
| 1111011001100 | 13 | 8 | 8047 (mod 8192) | 6561 | 9265 | 6 |
| 1111011010010 | 13 | 8 | 7791 (mod 8192) | 6561 | 9521 | 6 |
| 1111011010100 | 13 | 8 | 623 (mod 8192) | 6561 | 8497 | 6 |
| 1111011011000 | 13 | 8 | 1135 (mod 8192) | 6561 | 7985 | 5 |
| 1111011100010 | 13 | 8 | 4079 (mod 8192) | 6561 | 9137 | 6 |
| 1111011100100 | 13 | 8 | 5103 (mod 8192) | 6561 | 8113 | 5 |
| 1111011101000 | 13 | 8 | 5615 (mod 8192) | 6561 | 7601 | 5 |
| 1111011110000 | 13 | 8 | 5871 (mod 8192) | 6561 | 7345 | 5 |
| 1111100101010 | 13 | 8 | 1247 (mod 8192) | 6561 | 10433 | 7 |
| 1111100101100 | 13 | 8 | 2271 (mod 8192) | 6561 | 9409 | 6 |
| 1111100110010 | 13 | 8 | 2015 (mod 8192) | 6561 | 9665 | 6 |
| 1111100110100 | 13 | 8 | 3039 (mod 8192) | 6561 | 8641 | 6 |
| 1111100111000 | 13 | 8 | 3551 (mod 8192) | 6561 | 8129 | 5 |
| 1111101001010 | 13 | 8 | 7967 (mod 8192) | 6561 | 9857 | 7 |
| 1111101001100 | 13 | 8 | 799 (mod 8192) | 6561 | 8833 | 6 |
| 1111101010010 | 13 | 8 | 543 (mod 8192) | 6561 | 9089 | 6 |
| 1111101010100 | 13 | 8 | 1567 (mod 8192) | 6561 | 8065 | 5 |
| 1111101011000 | 13 | 8 | 2079 (mod 8192) | 6561 | 7553 | 5 |
| 1111101100010 | 13 | 8 | 5023 (mod 8192) | 6561 | 8705 | 6 |
| 1111101100100 | 13 | 8 | 6047 (mod 8192) | 6561 | 7681 | 5 |
| 1111101101000 | 13 | 8 | 6559 (mod 8192) | 6561 | 7169 | 5 |
| 1111101110000 | 13 | 8 | 6815 (mod 8192) | 6561 | 6913 | 5 |
| 1111110001010 | 13 | 8 | 3135 (mod 8192) | 6561 | 9569 | 6 |
| 1111110001100 | 13 | 8 | 4159 (mod 8192) | 6561 | 8545 | 6 |
| 1111110010010 | 13 | 8 | 3903 (mod 8192) | 6561 | 8801 | 6 |
| 1111110010100 | 13 | 8 | 4927 (mod 8192) | 6561 | 7777 | 5 |
| 1111110011000 | 13 | 8 | 5439 (mod 8192) | 6561 | 7265 | 5 |
| 1111110100010 | 13 | 8 | 191 (mod 8192) | 6561 | 8417 | 6 |
| 1111110100100 | 13 | 8 | 1215 (mod 8192) | 6561 | 7393 | 5 |
| 1111110101000 | 13 | 8 | 1727 (mod 8192) | 6561 | 6881 | 5 |
| 1111110110000 | 13 | 8 | 1983 (mod 8192) | 6561 | 6625 | 5 |
| 1111111000010 | 13 | 8 | 2431 (mod 8192) | 6561 | 8225 | 6 |
| 1111111000100 | 13 | 8 | 3455 (mod 8192) | 6561 | 7201 | 5 |
| 1111111001000 | 13 | 8 | 3967 (mod 8192) | 6561 | 6689 | 5 |
| 1111111010000 | 13 | 8 | 4223 (mod 8192) | 6561 | 6433 | 4 |
| 1111111100000 | 13 | 8 | 255 (mod 8192) | 6561 | 6305 | 4 |
| 110110110101100 | 15 | 9 | 7163 (mod 32768) | 19683 | 44143 | 4 |
| 110110110110100 | 15 | 9 | 8187 (mod 32768) | 19683 | 41071 | 4 |
| 110110110111000 | 15 | 9 | 30715 (mod 32768) | 19683 | 39023 | 3 |
| 110110111001100 | 15 | 9 | 16123 (mod 32768) | 19683 | 41839 | 4 |
| 110110111010100 | 15 | 9 | 17147 (mod 32768) | 19683 | 38767 | 3 |
| 110110111011000 | 15 | 9 | 6907 (mod 32768) | 19683 | 36719 | 3 |
| 110110111100100 | 15 | 9 | 1275 (mod 32768) | 19683 | 37231 | 3 |
| 110110111101000 | 15 | 9 | 23803 (mod 32768) | 19683 | 35183 | 3 |
| 110110111110000 | 15 | 9 | 2299 (mod 32768) | 19683 | 34159 | 3 |
| 110111010101100 | 15 | 9 | 9051 (mod 32768) | 19683 | 41551 | 4 |
| 110111010110100 | 15 | 9 | 10075 (mod 32768) | 19683 | 38479 | 3 |
| 110111010111000 | 15 | 9 | 32603 (mod 32768) | 19683 | 36431 | 3 |
| 110111011001100 | 15 | 9 | 18011 (mod 32768) | 19683 | 39247 | 3 |
| 110111011010100 | 15 | 9 | 19035 (mod 32768) | 19683 | 36175 | 3 |
| 110111011011000 | 15 | 9 | 8795 (mod 32768) | 19683 | 34127 | 3 |
| 110111011100100 | 15 | 9 | 3163 (mod 32768) | 19683 | 34639 | 3 |
| 110111011101000 | 15 | 9 | 25691 (mod 32768) | 19683 | 32591 | 3 |
| 110111011110000 | 15 | 9 | 4187 (mod 32768) | 19683 | 31567 | 3 |
| 110111100101100 | 15 | 9 | 32155 (mod 32768) | 19683 | 39823 | 4 |
| 110111100110100 | 15 | 9 | 411 (mod 32768) | 19683 | 36751 | 3 |
| 110111100111000 | 15 | 9 | 22939 (mod 32768) | 19683 | 34703 | 3 |
| 110111101001100 | 15 | 9 | 8347 (mod 32768) | 19683 | 37519 | 3 |
| 110111101010100 | 15 | 9 | 9371 (mod 32768) | 19683 | 34447 | 3 |
| 110111101011000 | 15 | 9 | 31899 (mod 32768) | 19683 | 32399 | 3 |
| 110111101100100 | 15 | 9 | 26267 (mod 32768) | 19683 | 32911 | 3 |
| 110111101101000 | 15 | 9 | 16027 (mod 32768) | 19683 | 30863 | 3 |
| 110111101110000 | 15 | 9 | 27291 (mod 32768) | 19683 | 29839 | 3 |
| 110111110001100 | 15 | 9 | 12827 (mod 32768) | 19683 | 36367 | 3 |
| 110111110010100 | 15 | 9 | 13851 (mod 32768) | 19683 | 33295 | 3 |
| 110111110011000 | 15 | 9 | 3611 (mod 32768) | 19683 | 31247 | 3 |
| 110111110100100 | 15 | 9 | 30747 (mod 32768) | 19683 | 31759 | 3 |
| 110111110101000 | 15 | 9 | 20507 (mod 32768) | 19683 | 29711 | 3 |
| 110111110110000 | 15 | 9 | 31771 (mod 32768) | 19683 | 28687 | 3 |
| 110111111000100 | 15 | 9 | 22811 (mod 32768) | 19683 | 30991 | 3 |
| 110111111001000 | 15 | 9 | 12571 (mod 32768) | 19683 | 28943 | 3 |
| 110111111010000 | 15 | 9 | 23835 (mod 32768) | 19683 | 27919 | 3 |
| 110111111100000 | 15 | 9 | 29467 (mod 32768) | 19683 | 27407 | 3 |
| 111010110101100 | 15 | 9 | 1095 (mod 32768) | 19683 | 41227 | 4 |
| 111010110110100 | 15 | 9 | 2119 (mod 32768) | 19683 | 38155 | 3 |
| 111010110111000 | 15 | 9 | 24647 (mod 32768) | 19683 | 36107 | 3 |
| 111010111001100 | 15 | 9 | 10055 (mod 32768) | 19683 | 38923 | 3 |
| 111010111010100 | 15 | 9 | 11079 (mod 32768) | 19683 | 35851 | 3 |
| 111010111011000 | 15 | 9 | 839 (mod 32768) | 19683 | 33803 | 3 |
| 111010111100100 | 15 | 9 | 27975 (mod 32768) | 19683 | 34315 | 3 |
| 111010111101000 | 15 | 9 | 17735 (mod 32768) | 19683 | 32267 | 3 |
| 111010111110000 | 15 | 9 | 28999 (mod 32768) | 19683 | 31243 | 3 |
| 111011010101100 | 15 | 9 | 2983 (mod 32768) | 19683 | 38635 | 3 |
| 111011010110100 | 15 | 9 | 4007 (mod 32768) | 19683 | 35563 | 3 |
| 111011010111000 | 15 | 9 | 26535 (mod 32768) | 19683 | 33515 | 3 |
| 111011011001100 | 15 | 9 | 11943 (mod 32768) | 19683 | 36331 | 3 |
| 111011011010100 | 15 | 9 | 12967 (mod 32768) | 19683 | 33259 | 3 |
| 111011011011000 | 15 | 9 | 2727 (mod 32768) | 19683 | 31211 | 3 |
| 111011011100100 | 15 | 9 | 29863 (mod 32768) | 19683 | 31723 | 3 |
| 111011011101000 | 15 | 9 | 19623 (mod 32768) | 19683 | 29675 | 3 |
| 111011011110000 | 15 | 9 | 30887 (mod 32768) | 19683 | 28651 | 3 |
| 111011100101100 | 15 | 9 | 26087 (mod 32768) | 19683 | 36907 | 3 |
| 111011100110100 | 15 | 9 | 27111 (mod 32768) | 19683 | 33835 | 3 |
| 111011100111000 | 15 | 9 | 16871 (mod 32768) | 19683 | 31787 | 3 |
| 111011101001100 | 15 | 9 | 2279 (mod 32768) | 19683 | 34603 | 3 |
| 111011101010100 | 15 | 9 | 3303 (mod 32768) | 19683 | 31531 | 3 |
| 111011101011000 | 15 | 9 | 25831 (mod 32768) | 19683 | 29483 | 3 |
| 111011101100100 | 15 | 9 | 20199 (mod 32768) | 19683 | 29995 | 3 |
| 111011101101000 | 15 | 9 | 9959 (mod 32768) | 19683 | 27947 | 3 |
| 111011101110000 | 15 | 9 | 21223 (mod 32768) | 19683 | 26923 | 3 |
| 111011110001100 | 15 | 9 | 6759 (mod 32768) | 19683 | 33451 | 3 |
| 111011110010100 | 15 | 9 | 7783 (mod 32768) | 19683 | 30379 | 3 |
| 111011110011000 | 15 | 9 | 30311 (mod 32768) | 19683 | 28331 | 3 |
| 111011110100100 | 15 | 9 | 24679 (mod 32768) | 19683 | 28843 | 3 |
| 111011110101000 | 15 | 9 | 14439 (mod 32768) | 19683 | 26795 | 3 |
| 111011110110000 | 15 | 9 | 25703 (mod 32768) | 19683 | 25771 | 2 |
| 111011111000100 | 15 | 9 | 16743 (mod 32768) | 19683 | 28075 | 3 |
| 111011111001000 | 15 | 9 | 6503 (mod 32768) | 19683 | 26027 | 2 |
| 111011111010000 | 15 | 9 | 17767 (mod 32768) | 19683 | 25003 | 2 |
| 111011111100000 | 15 | 9 | 23399 (mod 32768) | 19683 | 24491 | 2 |
| 111100110101100 | 15 | 9 | 18895 (mod 32768) | 19683 | 39283 | 4 |
| 111100110110100 | 15 | 9 | 19919 (mod 32768) | 19683 | 36211 | 3 |
| 111100110111000 | 15 | 9 | 9679 (mod 32768) | 19683 | 34163 | 3 |
| 111100111001100 | 15 | 9 | 27855 (mod 32768) | 19683 | 36979 | 3 |
| 111100111010100 | 15 | 9 | 28879 (mod 32768) | 19683 | 33907 | 3 |
| 111100111011000 | 15 | 9 | 18639 (mod 32768) | 19683 | 31859 | 3 |
| 111100111100100 | 15 | 9 | 13007 (mod 32768) | 19683 | 32371 | 3 |
| 111100111101000 | 15 | 9 | 2767 (mod 32768) | 19683 | 30323 | 3 |
| 111100111110000 | 15 | 9 | 14031 (mod 32768) | 19683 | 29299 | 3 |
| 111101010101100 | 15 | 9 | 20783 (mod 32768) | 19683 | 36691 | 3 |
| 111101010110100 | 15 | 9 | 21807 (mod 32768) | 19683 | 33619 | 3 |
| 111101010111000 | 15 | 9 | 11567 (mod 32768) | 19683 | 31571 | 3 |
| 111101011001100 | 15 | 9 | 29743 (mod 32768) | 19683 | 34387 | 3 |
| 111101011010100 | 15 | 9 | 30767 (mod 32768) | 19683 | 31315 | 3 |
| 111101011011000 | 15 | 9 | 20527 (mod 32768) | 19683 | 29267 | 3 |
| 111101011100100 | 15 | 9 | 14895 (mod 32768) | 19683 | 29779 | 3 |
| 111101011101000 | 15 | 9 | 4655 (mod 32768) | 19683 | 27731 | 3 |
| 111101011110000 | 15 | 9 | 15919 (mod 32768) | 19683 | 26707 | 3 |
| 111101100101100 | 15 | 9 | 11119 (mod 32768) | 19683 | 34963 | 3 |
| 111101100110100 | 15 | 9 | 12143 (mod 32768) | 19683 | 31891 | 3 |
| 111101100111000 | 15 | 9 | 1903 (mod 32768) | 19683 | 29843 | 3 |
| 111101101001100 | 15 | 9 | 20079 (mod 32768) | 19683 | 32659 | 3 |
| 111101101010100 | 15 | 9 | 21103 (mod 32768) | 19683 | 29587 | 3 |
| 111101101011000 | 15 | 9 | 10863 (mod 32768) | 19683 | 27539 | 3 |
| 111101101100100 | 15 | 9 | 5231 (mod 32768) | 19683 | 28051 | 3 |
| 111101101101000 | 15 | 9 | 27759 (mod 32768) | 19683 | 26003 | 2 |
| 111101101110000 | 15 | 9 | 6255 (mod 32768) | 19683 | 24979 | 2 |
| 111101110001100 | 15 | 9 | 24559 (mod 32768) | 19683 | 31507 | 3 |
| 111101110010100 | 15 | 9 | 25583 (mod 32768) | 19683 | 28435 | 3 |
| 111101110011000 | 15 | 9 | 15343 (mod 32768) | 19683 | 26387 | 3 |
| 111101110100100 | 15 | 9 | 9711 (mod 32768) | 19683 | 26899 | 3 |
| 111101110101000 | 15 | 9 | 32239 (mod 32768) | 19683 | 24851 | 2 |
| 111101110110000 | 15 | 9 | 10735 (mod 32768) | 19683 | 23827 | 2 |
| 111101111000100 | 15 | 9 | 1775 (mod 32768) | 19683 | 26131 | 2 |
| 111101111001000 | 15 | 9 | 24303 (mod 32768) | 19683 | 24083 | 2 |
| 111101111010000 | 15 | 9 | 2799 (mod 32768) | 19683 | 23059 | 2 |
| 111101111100000 | 15 | 9 | 8431 (mod 32768) | 19683 | 22547 | 2 |
| 111110010101100 | 15 | 9 | 21727 (mod 32768) | 19683 | 35395 | 3 |
| 111110010110100 | 15 | 9 | 22751 (mod 32768) | 19683 | 32323 | 3 |
| 111110010111000 | 15 | 9 | 12511 (mod 32768) | 19683 | 30275 | 3 |
| 111110011001100 | 15 | 9 | 30687 (mod 32768) | 19683 | 33091 | 3 |
| 111110011010100 | 15 | 9 | 31711 (mod 32768) | 19683 | 30019 | 3 |
| 111110011011000 | 15 | 9 | 21471 (mod 32768) | 19683 | 27971 | 3 |
| 111110011100100 | 15 | 9 | 15839 (mod 32768) | 19683 | 28483 | 3 |
| 111110011101000 | 15 | 9 | 5599 (mod 32768) | 19683 | 26435 | 3 |
| 111110011110000 | 15 | 9 | 16863 (mod 32768) | 19683 | 25411 | 2 |
| 111110100101100 | 15 | 9 | 12063 (mod 32768) | 19683 | 33667 | 3 |
| 111110100110100 | 15 | 9 | 13087 (mod 32768) | 19683 | 30595 | 3 |
| 111110100111000 | 15 | 9 | 2847 (mod 32768) | 19683 | 28547 | 3 |
| 111110101001100 | 15 | 9 | 21023 (mod 32768) | 19683 | 31363 | 3 |
| 111110101010100 | 15 | 9 | 22047 (mod 32768) | 19683 | 28291 | 3 |
| 111110101011000 | 15 | 9 | 11807 (mod 32768) | 19683 | 26243 | 3 |
| 111110101100100 | 15 | 9 | 6175 (mod 32768) | 19683 | 26755 | 3 |
| 111110101101000 | 15 | 9 | 28703 (mod 32768) | 19683 | 24707 | 2 |
| 111110101110000 | 15 | 9 | 7199 (mod 32768) | 19683 | 23683 | 2 |
| 111110110001100 | 15 | 9 | 25503 (mod 32768) | 19683 | 30211 | 3 |
| 111110110010100 | 15 | 9 | 26527 (mod 32768) | 19683 | 27139 | 3 |
| 111110110011000 | 15 | 9 | 16287 (mod 32768) | 19683 | 25091 | 2 |
| 111110110100100 | 15 | 9 | 10655 (mod 32768) | 19683 | 25603 | 2 |
| 111110110101000 | 15 | 9 | 415 (mod 32768) | 19683 | 23555 | 2 |
| 111110110110000 | 15 | 9 | 11679 (mod 32768) | 19683 | 22531 | 2 |
| 111110111000100 | 15 | 9 | 2719 (mod 32768) | 19683 | 24835 | 2 |
| 111110111001000 | 15 | 9 | 25247 (mod 32768) | 19683 | 22787 | 2 |
| 111110111010000 | 15 | 9 | 3743 (mod 32768) | 19683 | 21763 | 2 |
| 111110111100000 | 15 | 9 | 9375 (mod 32768) | 19683 | 21251 | 2 |
| 111111000101100 | 15 | 9 | 23615 (mod 32768) | 19683 | 32803 | 3 |
| 111111000110100 | 15 | 9 | 24639 (mod 32768) | 19683 | 29731 | 3 |
| 111111000111000 | 15 | 9 | 14399 (mod 32768) | 19683 | 27683 | 3 |
| 111111001001100 | 15 | 9 | 32575 (mod 32768) | 19683 | 30499 | 3 |
| 111111001010100 | 15 | 9 | 831 (mod 32768) | 19683 | 27427 | 3 |
| 111111001011000 | 15 | 9 | 23359 (mod 32768) | 19683 | 25379 | 2 |
| 111111001100100 | 15 | 9 | 17727 (mod 32768) | 19683 | 25891 | 2 |
| 111111001101000 | 15 | 9 | 7487 (mod 32768) | 19683 | 23843 | 2 |
| 111111001110000 | 15 | 9 | 18751 (mod 32768) | 19683 | 22819 | 2 |
| 111111010001100 | 15 | 9 | 4287 (mod 32768) | 19683 | 29347 | 3 |
| 111111010010100 | 15 | 9 | 5311 (mod 32768) | 19683 | 26275 | 3 |
| 111111010011000 | 15 | 9 | 27839 (mod 32768) | 19683 | 24227 | 2 |
| 111111010100100 | 15 | 9 | 22207 (mod 32768) | 19683 | 24739 | 2 |
| 111111010101000 | 15 | 9 | 11967 (mod 32768) | 19683 | 22691 | 2 |
| 111111010110000 | 15 | 9 | 23231 (mod 32768) | 19683 | 21667 | 2 |
| 111111011000100 | 15 | 9 | 14271 (mod 32768) | 19683 | 23971 | 2 |
| 111111011001000 | 15 | 9 | 4031 (mod 32768) | 19683 | 21923 | 2 |
| 111111011010000 | 15 | 9 | 15295 (mod 32768) | 19683 | 20899 | 2 |
| 111111011100000 | 15 | 9 | 20927 (mod 32768) | 19683 | 20387 | 2 |
| 111111100001100 | 15 | 9 | 22911 (mod 32768) | 19683 | 28771 | 3 |
| 111111100010100 | 15 | 9 | 23935 (mod 32768) | 19683 | 25699 | 2 |
| 111111100011000 | 15 | 9 | 13695 (mod 32768) | 19683 | 23651 | 2 |
| 111111100100100 | 15 | 9 | 8063 (mod 32768) | 19683 | 24163 | 2 |
| 111111100101000 | 15 | 9 | 30591 (mod 32768) | 19683 | 22115 | 2 |
| 111111100110000 | 15 | 9 | 9087 (mod 32768) | 19683 | 21091 | 2 |
| 111111101000100 | 15 | 9 | 127 (mod 32768) | 19683 | 23395 | 2 |
| 111111101001000 | 15 | 9 | 22655 (mod 32768) | 19683 | 21347 | 2 |
| 111111101010000 | 15 | 9 | 1151 (mod 32768) | 19683 | 20323 | 2 |
| 111111101100000 | 15 | 9 | 6783 (mod 32768) | 19683 | 19811 | 2 |
| 111111110000100 | 15 | 9 | 12543 (mod 32768) | 19683 | 23011 | 2 |
| 111111110001000 | 15 | 9 | 2303 (mod 32768) | 19683 | 20963 | 2 |
| 111111110010000 | 15 | 9 | 13567 (mod 32768) | 19683 | 19939 | 2 |
| 111111110100000 | 15 | 9 | 19199 (mod 32768) | 19683 | 19427 | 2 |
| 111111111000000 | 15 | 9 | 5631 (mod 32768) | 19683 | 19171 | 2 |
| 1101101101011010 | 16 | 10 | 56315 (mod 65536) | 59049 | 148813 | 23 |
| 1101101101011100 | 16 | 10 | 64507 (mod 65536) | 59049 | 140621 | 22 |
| 1101101101101010 | 16 | 10 | 24571 (mod 65536) | 59049 | 139597 | 22 |
| 1101101101101100 | 16 | 10 | 32763 (mod 65536) | 59049 | 131405 | 21 |
| 1101101101110010 | 16 | 10 | 47099 (mod 65536) | 59049 | 133453 | 21 |
| 1101101101110100 | 16 | 10 | 55291 (mod 65536) | 59049 | 125261 | 20 |
| 1101101101111000 | 16 | 10 | 26619 (mod 65536) | 59049 | 121165 | 19 |
| 1101101110011010 | 16 | 10 | 65275 (mod 65536) | 59049 | 141901 | 22 |
| 1101101110011100 | 16 | 10 | 7931 (mod 65536) | 59049 | 133709 | 21 |
| 1101101110101010 | 16 | 10 | 33531 (mod 65536) | 59049 | 132685 | 21 |
| 1101101110101100 | 16 | 10 | 41723 (mod 65536) | 59049 | 124493 | 20 |
| 1101101110110010 | 16 | 10 | 56059 (mod 65536) | 59049 | 126541 | 20 |
| 1101101110110100 | 16 | 10 | 64251 (mod 65536) | 59049 | 118349 | 19 |
| 1101101110111000 | 16 | 10 | 35579 (mod 65536) | 59049 | 114253 | 18 |
| 1101101111001010 | 16 | 10 | 17659 (mod 65536) | 59049 | 128077 | 20 |
| 1101101111001100 | 16 | 10 | 25851 (mod 65536) | 59049 | 119885 | 19 |
| 1101101111010010 | 16 | 10 | 40187 (mod 65536) | 59049 | 121933 | 19 |
| 1101101111010100 | 16 | 10 | 48379 (mod 65536) | 59049 | 113741 | 18 |
| 1101101111011000 | 16 | 10 | 19707 (mod 65536) | 59049 | 109645 | 17 |
| 1101101111100010 | 16 | 10 | 51451 (mod 65536) | 59049 | 118861 | 19 |
| 1101101111100100 | 16 | 10 | 59643 (mod 65536) | 59049 | 110669 | 18 |
| 1101101111101000 | 16 | 10 | 30971 (mod 65536) | 59049 | 106573 | 17 |
| 1101101111110000 | 16 | 10 | 16635 (mod 65536) | 59049 | 104525 | 17 |
| 1101110101011010 | 16 | 10 | 58203 (mod 65536) | 59049 | 141037 | 22 |
| 1101110101011100 | 16 | 10 | 859 (mod 65536) | 59049 | 132845 | 21 |
| 1101110101101010 | 16 | 10 | 26459 (mod 65536) | 59049 | 131821 | 21 |
| 1101110101101100 | 16 | 10 | 34651 (mod 65536) | 59049 | 123629 | 20 |
| 1101110101110010 | 16 | 10 | 48987 (mod 65536) | 59049 | 125677 | 20 |
| 1101110101110100 | 16 | 10 | 57179 (mod 65536) | 59049 | 117485 | 19 |
| 1101110101111000 | 16 | 10 | 28507 (mod 65536) | 59049 | 113389 | 18 |
| 1101110110011010 | 16 | 10 | 1627 (mod 65536) | 59049 | 134125 | 21 |
| 1101110110011100 | 16 | 10 | 9819 (mod 65536) | 59049 | 125933 | 20 |
| 1101110110101010 | 16 | 10 | 35419 (mod 65536) | 59049 | 124909 | 20 |
| 1101110110101100 | 16 | 10 | 43611 (mod 65536) | 59049 | 116717 | 18 |
| 1101110110110010 | 16 | 10 | 57947 (mod 65536) | 59049 | 118765 | 19 |
| 1101110110110100 | 16 | 10 | 603 (mod 65536) | 59049 | 110573 | 18 |
| 1101110110111000 | 16 | 10 | 37467 (mod 65536) | 59049 | 106477 | 17 |
| 1101110111001010 | 16 | 10 | 19547 (mod 65536) | 59049 | 120301 | 19 |
| 1101110111001100 | 16 | 10 | 27739 (mod 65536) | 59049 | 112109 | 18 |
| 1101110111010010 | 16 | 10 | 42075 (mod 65536) | 59049 | 114157 | 18 |
| 1101110111010100 | 16 | 10 | 50267 (mod 65536) | 59049 | 105965 | 17 |
| 1101110111011000 | 16 | 10 | 21595 (mod 65536) | 59049 | 101869 | 16 |
| 1101110111100010 | 16 | 10 | 53339 (mod 65536) | 59049 | 111085 | 18 |
| 1101110111100100 | 16 | 10 | 61531 (mod 65536) | 59049 | 102893 | 16 |
| 1101110111101000 | 16 | 10 | 32859 (mod 65536) | 59049 | 98797 | 16 |
| 1101110111110000 | 16 | 10 | 18523 (mod 65536) | 59049 | 96749 | 15 |
| 1101111001011010 | 16 | 10 | 15771 (mod 65536) | 59049 | 135853 | 21 |
| 1101111001011100 | 16 | 10 | 23963 (mod 65536) | 59049 | 127661 | 20 |
| 1101111001101010 | 16 | 10 | 49563 (mod 65536) | 59049 | 126637 | 20 |
| 1101111001101100 | 16 | 10 | 57755 (mod 65536) | 59049 | 118445 | 19 |
| 1101111001110010 | 16 | 10 | 6555 (mod 65536) | 59049 | 120493 | 19 |
| 1101111001110100 | 16 | 10 | 14747 (mod 65536) | 59049 | 112301 | 18 |
| 1101111001111000 | 16 | 10 | 51611 (mod 65536) | 59049 | 108205 | 17 |
| 1101111010011010 | 16 | 10 | 24731 (mod 65536) | 59049 | 128941 | 20 |
| 1101111010011100 | 16 | 10 | 32923 (mod 65536) | 59049 | 120749 | 19 |
| 1101111010101010 | 16 | 10 | 58523 (mod 65536) | 59049 | 119725 | 19 |
| 1101111010101100 | 16 | 10 | 1179 (mod 65536) | 59049 | 111533 | 18 |
| 1101111010110010 | 16 | 10 | 15515 (mod 65536) | 59049 | 113581 | 18 |
| 1101111010110100 | 16 | 10 | 23707 (mod 65536) | 59049 | 105389 | 17 |
| 1101111010111000 | 16 | 10 | 60571 (mod 65536) | 59049 | 101293 | 16 |
| 1101111011001010 | 16 | 10 | 42651 (mod 65536) | 59049 | 115117 | 18 |
| 1101111011001100 | 16 | 10 | 50843 (mod 65536) | 59049 | 106925 | 17 |
| 1101111011010010 | 16 | 10 | 65179 (mod 65536) | 59049 | 108973 | 17 |
| 1101111011010100 | 16 | 10 | 7835 (mod 65536) | 59049 | 100781 | 16 |
| 1101111011011000 | 16 | 10 | 44699 (mod 65536) | 59049 | 96685 | 15 |
| 1101111011100010 | 16 | 10 | 10907 (mod 65536) | 59049 | 105901 | 17 |
| 1101111011100100 | 16 | 10 | 19099 (mod 65536) | 59049 | 97709 | 16 |
| 1101111011101000 | 16 | 10 | 55963 (mod 65536) | 59049 | 93613 | 15 |
| 1101111011110000 | 16 | 10 | 41627 (mod 65536) | 59049 | 91565 | 15 |
| 1101111100011010 | 16 | 10 | 61979 (mod 65536) | 59049 | 125485 | 20 |
| 1101111100011100 | 16 | 10 | 4635 (mod 65536) | 59049 | 117293 | 19 |
| 1101111100101010 | 16 | 10 | 30235 (mod 65536) | 59049 | 116269 | 18 |
| 1101111100101100 | 16 | 10 | 38427 (mod 65536) | 59049 | 108077 | 17 |
| 1101111100110010 | 16 | 10 | 52763 (mod 65536) | 59049 | 110125 | 17 |
| 1101111100110100 | 16 | 10 | 60955 (mod 65536) | 59049 | 101933 | 16 |
| 1101111100111000 | 16 | 10 | 32283 (mod 65536) | 59049 | 97837 | 16 |
| 1101111101001010 | 16 | 10 | 14363 (mod 65536) | 59049 | 111661 | 18 |
| 1101111101001100 | 16 | 10 | 22555 (mod 65536) | 59049 | 103469 | 16 |
| 1101111101010010 | 16 | 10 | 36891 (mod 65536) | 59049 | 105517 | 17 |
| 1101111101010100 | 16 | 10 | 45083 (mod 65536) | 59049 | 97325 | 16 |
| 1101111101011000 | 16 | 10 | 16411 (mod 65536) | 59049 | 93229 | 15 |
| 1101111101100010 | 16 | 10 | 48155 (mod 65536) | 59049 | 102445 | 16 |
| 1101111101100100 | 16 | 10 | 56347 (mod 65536) | 59049 | 94253 | 15 |
| 1101111101101000 | 16 | 10 | 27675 (mod 65536) | 59049 | 90157 | 14 |
| 1101111101110000 | 16 | 10 | 13339 (mod 65536) | 59049 | 88109 | 14 |
| 1101111110001010 | 16 | 10 | 39195 (mod 65536) | 59049 | 109357 | 17 |
| 1101111110001100 | 16 | 10 | 47387 (mod 65536) | 59049 | 101165 | 16 |
| 1101111110010010 | 16 | 10 | 61723 (mod 65536) | 59049 | 103213 | 16 |
| 1101111110010100 | 16 | 10 | 4379 (mod 65536) | 59049 | 95021 | 15 |
| 1101111110011000 | 16 | 10 | 41243 (mod 65536) | 59049 | 90925 | 15 |
| 1101111110100010 | 16 | 10 | 7451 (mod 65536) | 59049 | 100141 | 16 |
| 1101111110100100 | 16 | 10 | 15643 (mod 65536) | 59049 | 91949 | 15 |
| 1101111110101000 | 16 | 10 | 52507 (mod 65536) | 59049 | 87853 | 14 |
| 1101111110110000 | 16 | 10 | 38171 (mod 65536) | 59049 | 85805 | 14 |
| 1101111111000010 | 16 | 10 | 45851 (mod 65536) | 59049 | 98605 | 16 |
| 1101111111000100 | 16 | 10 | 54043 (mod 65536) | 59049 | 90413 | 14 |
| 1101111111001000 | 16 | 10 | 25371 (mod 65536) | 59049 | 86317 | 14 |
| 1101111111010000 | 16 | 10 | 11035 (mod 65536) | 59049 | 84269 | 13 |
| 1101111111100000 | 16 | 10 | 36635 (mod 65536) | 59049 | 83245 | 13 |
| 1110101101011010 | 16 | 10 | 17479 (mod 65536) | 59049 | 140065 | 22 |
| 1110101101011100 | 16 | 10 | 25671 (mod 65536) | 59049 | 131873 | 21 |
| 1110101101101010 | 16 | 10 | 51271 (mod 65536) | 59049 | 130849 | 21 |
| 1110101101101100 | 16 | 10 | 59463 (mod 65536) | 59049 | 122657 | 19 |
| 1110101101110010 | 16 | 10 | 8263 (mod 65536) | 59049 | 124705 | 20 |
| 1110101101110100 | 16 | 10 | 16455 (mod 65536) | 59049 | 116513 | 18 |
| 1110101101111000 | 16 | 10 | 53319 (mod 65536) | 59049 | 112417 | 18 |
| 1110101110011010 | 16 | 10 | 26439 (mod 65536) | 59049 | 133153 | 21 |
| 1110101110011100 | 16 | 10 | 34631 (mod 65536) | 59049 | 124961 | 20 |
| 1110101110101010 | 16 | 10 | 60231 (mod 65536) | 59049 | 123937 | 20 |
| 1110101110101100 | 16 | 10 | 2887 (mod 65536) | 59049 | 115745 | 18 |
| 1110101110110010 | 16 | 10 | 17223 (mod 65536) | 59049 | 117793 | 19 |
| 1110101110110100 | 16 | 10 | 25415 (mod 65536) | 59049 | 109601 | 17 |
| 1110101110111000 | 16 | 10 | 62279 (mod 65536) | 59049 | 105505 | 17 |
| 1110101111001010 | 16 | 10 | 44359 (mod 65536) | 59049 | 119329 | 19 |
| 1110101111001100 | 16 | 10 | 52551 (mod 65536) | 59049 | 111137 | 18 |
| 1110101111010010 | 16 | 10 | 1351 (mod 65536) | 59049 | 113185 | 18 |
| 1110101111010100 | 16 | 10 | 9543 (mod 65536) | 59049 | 104993 | 17 |
| 1110101111011000 | 16 | 10 | 46407 (mod 65536) | 59049 | 100897 | 16 |
| 1110101111100010 | 16 | 10 | 12615 (mod 65536) | 59049 | 110113 | 17 |
| 1110101111100100 | 16 | 10 | 20807 (mod 65536) | 59049 | 101921 | 16 |
| 1110101111101000 | 16 | 10 | 57671 (mod 65536) | 59049 | 97825 | 16 |
| 1110101111110000 | 16 | 10 | 43335 (mod 65536) | 59049 | 95777 | 15 |
| 1110110101011010 | 16 | 10 | 19367 (mod 65536) | 59049 | 132289 | 21 |
| 1110110101011100 | 16 | 10 | 27559 (mod 65536) | 59049 | 124097 | 20 |
| 1110110101101010 | 16 | 10 | 53159 (mod 65536) | 59049 | 123073 | 19 |
| 1110110101101100 | 16 | 10 | 61351 (mod 65536) | 59049 | 114881 | 18 |
| 1110110101110010 | 16 | 10 | 10151 (mod 65536) | 59049 | 116929 | 19 |
| 1110110101110100 | 16 | 10 | 18343 (mod 65536) | 59049 | 108737 | 17 |
| 1110110101111000 | 16 | 10 | 55207 (mod 65536) | 59049 | 104641 | 17 |
| 1110110110011010 | 16 | 10 | 28327 (mod 65536) | 59049 | 125377 | 20 |
| 1110110110011100 | 16 | 10 | 36519 (mod 65536) | 59049 | 117185 | 19 |
| 1110110110101010 | 16 | 10 | 62119 (mod 65536) | 59049 | 116161 | 18 |
| 1110110110101100 | 16 | 10 | 4775 (mod 65536) | 59049 | 107969 | 17 |
| 1110110110110010 | 16 | 10 | 19111 (mod 65536) | 59049 | 110017 | 17 |
| 1110110110110100 | 16 | 10 | 27303 (mod 65536) | 59049 | 101825 | 16 |
| 1110110110111000 | 16 | 10 | 64167 (mod 65536) | 59049 | 97729 | 16 |
| 1110110111001010 | 16 | 10 | 46247 (mod 65536) | 59049 | 111553 | 18 |
| 1110110111001100 | 16 | 10 | 54439 (mod 65536) | 59049 | 103361 | 16 |
| 1110110111010010 | 16 | 10 | 3239 (mod 65536) | 59049 | 105409 | 17 |
| 1110110111010100 | 16 | 10 | 11431 (mod 65536) | 59049 | 97217 | 15 |
| 1110110111011000 | 16 | 10 | 48295 (mod 65536) | 59049 | 93121 | 15 |
| 1110110111100010 | 16 | 10 | 14503 (mod 65536) | 59049 | 102337 | 16 |
| 1110110111100100 | 16 | 10 | 22695 (mod 65536) | 59049 | 94145 | 15 |
| 1110110111101000 | 16 | 10 | 59559 (mod 65536) | 59049 | 90049 | 14 |
| 1110110111110000 | 16 | 10 | 45223 (mod 65536) | 59049 | 88001 | 14 |
| 1110111001011010 | 16 | 10 | 42471 (mod 65536) | 59049 | 127105 | 20 |
| 1110111001011100 | 16 | 10 | 50663 (mod 65536) | 59049 | 118913 | 19 |
| 1110111001101010 | 16 | 10 | 10727 (mod 65536) | 59049 | 117889 | 19 |
| 1110111001101100 | 16 | 10 | 18919 (mod 65536) | 59049 | 109697 | 17 |
| 1110111001110010 | 16 | 10 | 33255 (mod 65536) | 59049 | 111745 | 18 |
| 1110111001110100 | 16 | 10 | 41447 (mod 65536) | 59049 | 103553 | 16 |
| 1110111001111000 | 16 | 10 | 12775 (mod 65536) | 59049 | 99457 | 16 |
| 1110111010011010 | 16 | 10 | 51431 (mod 65536) | 59049 | 120193 | 19 |
| 1110111010011100 | 16 | 10 | 59623 (mod 65536) | 59049 | 112001 | 18 |
| 1110111010101010 | 16 | 10 | 19687 (mod 65536) | 59049 | 110977 | 18 |
| 1110111010101100 | 16 | 10 | 27879 (mod 65536) | 59049 | 102785 | 16 |
| 1110111010110010 | 16 | 10 | 42215 (mod 65536) | 59049 | 104833 | 17 |
| 1110111010110100 | 16 | 10 | 50407 (mod 65536) | 59049 | 96641 | 15 |
| 1110111010111000 | 16 | 10 | 21735 (mod 65536) | 59049 | 92545 | 15 |
| 1110111011001010 | 16 | 10 | 3815 (mod 65536) | 59049 | 106369 | 17 |
| 1110111011001100 | 16 | 10 | 12007 (mod 65536) | 59049 | 98177 | 16 |
| 1110111011010010 | 16 | 10 | 26343 (mod 65536) | 59049 | 100225 | 16 |
| 1110111011010100 | 16 | 10 | 34535 (mod 65536) | 59049 | 92033 | 15 |
| 1110111011011000 | 16 | 10 | 5863 (mod 65536) | 59049 | 87937 | 14 |
| 1110111011100010 | 16 | 10 | 37607 (mod 65536) | 59049 | 97153 | 15 |
| 1110111011100100 | 16 | 10 | 45799 (mod 65536) | 59049 | 88961 | 14 |
| 1110111011101000 | 16 | 10 | 17127 (mod 65536) | 59049 | 84865 | 14 |
| 1110111011110000 | 16 | 10 | 2791 (mod 65536) | 59049 | 82817 | 13 |
| 1110111100011010 | 16 | 10 | 23143 (mod 65536) | 59049 | 116737 | 18 |
| 1110111100011100 | 16 | 10 | 31335 (mod 65536) | 59049 | 108545 | 17 |
| 1110111100101010 | 16 | 10 | 56935 (mod 65536) | 59049 | 107521 | 17 |
| 1110111100101100 | 16 | 10 | 65127 (mod 65536) | 59049 | 99329 | 16 |
| 1110111100110010 | 16 | 10 | 13927 (mod 65536) | 59049 | 101377 | 16 |
| 1110111100110100 | 16 | 10 | 22119 (mod 65536) | 59049 | 93185 | 15 |
| 1110111100111000 | 16 | 10 | 58983 (mod 65536) | 59049 | 89089 | 14 |
| 1110111101001010 | 16 | 10 | 41063 (mod 65536) | 59049 | 102913 | 16 |
| 1110111101001100 | 16 | 10 | 49255 (mod 65536) | 59049 | 94721 | 15 |
| 1110111101010010 | 16 | 10 | 63591 (mod 65536) | 59049 | 96769 | 15 |
| 1110111101010100 | 16 | 10 | 6247 (mod 65536) | 59049 | 88577 | 14 |
| 1110111101011000 | 16 | 10 | 43111 (mod 65536) | 59049 | 84481 | 14 |
| 1110111101100010 | 16 | 10 | 9319 (mod 65536) | 59049 | 93697 | 15 |
| 1110111101100100 | 16 | 10 | 17511 (mod 65536) | 59049 | 85505 | 14 |
| 1110111101101000 | 16 | 10 | 54375 (mod 65536) | 59049 | 81409 | 13 |
| 1110111101110000 | 16 | 10 | 40039 (mod 65536) | 59049 | 79361 | 13 |
| 1110111110001010 | 16 | 10 | 359 (mod 65536) | 59049 | 100609 | 16 |
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| 1111111011100000 | 16 | 10 | 13951 (mod 65536) | 59049 | 60457 | 10 |
| 1111111100001010 | 16 | 10 | 28927 (mod 65536) | 59049 | 85417 | 14 |
| 1111111100001100 | 16 | 10 | 37119 (mod 65536) | 59049 | 77225 | 12 |
| 1111111100010010 | 16 | 10 | 51455 (mod 65536) | 59049 | 79273 | 13 |
| 1111111100010100 | 16 | 10 | 59647 (mod 65536) | 59049 | 71081 | 11 |
| 1111111100011000 | 16 | 10 | 30975 (mod 65536) | 59049 | 66985 | 11 |
| 1111111100100010 | 16 | 10 | 62719 (mod 65536) | 59049 | 76201 | 12 |
| 1111111100100100 | 16 | 10 | 5375 (mod 65536) | 59049 | 68009 | 11 |
| 1111111100101000 | 16 | 10 | 42239 (mod 65536) | 59049 | 63913 | 10 |
| 1111111100110000 | 16 | 10 | 27903 (mod 65536) | 59049 | 61865 | 10 |
| 1111111101000010 | 16 | 10 | 35583 (mod 65536) | 59049 | 74665 | 12 |
| 1111111101000100 | 16 | 10 | 43775 (mod 65536) | 59049 | 66473 | 11 |
| 1111111101001000 | 16 | 10 | 15103 (mod 65536) | 59049 | 62377 | 10 |
| 1111111101010000 | 16 | 10 | 767 (mod 65536) | 59049 | 60329 | 10 |
| 1111111101100000 | 16 | 10 | 26367 (mod 65536) | 59049 | 59305 | 10 |
| 1111111110000010 | 16 | 10 | 22015 (mod 65536) | 59049 | 73897 | 12 |
| 1111111110000100 | 16 | 10 | 30207 (mod 65536) | 59049 | 65705 | 11 |
| 1111111110001000 | 16 | 10 | 1535 (mod 65536) | 59049 | 61609 | 10 |
| 1111111110010000 | 16 | 10 | 52735 (mod 65536) | 59049 | 59561 | 10 |
| 1111111110100000 | 16 | 10 | 12799 (mod 65536) | 59049 | 58537 | 10 |
| 1111111111000000 | 16 | 10 | 25599 (mod 65536) | 59049 | 58025 | 9 |
Classes non fermées à profondeur 16 (liste exhaustive)
Chaque élément ci‑dessous est un mot de parité de longueur 16 correspondant à une unique classe modulo 2^16 qui n’a pas été fermée par la condition de contraction locale avant la profondeur maximale.
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