| Radix Character Encoding | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V |
| W | X | Y | Z | a | b | c | d | e | f | g | h | i | j | k | l |
| m | n | o | p | q | r | s | t | u | v | w | x | y | z | Α | Β |
| Γ | Δ | Ε | Ζ | Η | Θ | Ι | Κ | Λ | Μ | Ν | Ξ | Ο | Π | Ρ | Σ |
| Color Key | ||
|---|---|---|
| Orange | Fixed Point | number that becomes itself after one iteration |
| Green | Final Numbers | all numbers eventually reached, from all cycles |
| Purple | Cycle Start | iterations include entry into cycle, assuming it repeats |
| Red | Full Cycle | iterations include entire cycle, proving it repeats |
| Blue | Start Numbers | subset (optimization) of all numbers; minimal for full coverage |
| Gray | No Results | any calculation that has no results |
| Digits | # Full Cycles (excluding zero) |
Frequency | Cycle Length |
Full Cycles (excluding zero) (bold = exactly one cycle [excluding zero]) |
|---|---|---|---|---|
| 1 | 0 cycles | - | - | - |
| 2 | 2 cycles | 1,056× | (max) 4 nodes | ⮎ 3Β → x7 → pF → ZV ⮌ |
| 1,056× | (max) 4 nodes | ⮎ Bt → hN → Jl → Rd ⮌ | ||
| 3 | 1 cycle | 52,327× | (max) 2 nodes | ⮎ WΕY → XΕX ⮌ |
| 4 | 16 cycles | 58,349× | (max) 33 nodes | ⮎ F6xq → raTE → d6xS → rAtE → jcRM → NAti → jKjM → PMhg → LGnk → XOfY → H0Δo → ΔWX2 → Β0Δ4 → Δw72 → ΒoF4 → xYV8 → p2ΒG → zYV6 → t2ΒC → zgN6 → tIlC → hSbO → J8vm → nSbI → V8va → n4zI → vUZA → l4zK → vQdA → lCrK → fQdQ → FCrq → faTQ ⮌ |
| 58,349× | (max) 33 nodes | ⮎ B8vu → niLI → VMha → L4zk → vOfA → lGnK → XQdY → D0Δs → ΔeP2 → ΒEp4 → xaT8 → p6xG → rYVE → d2ΒS → zAt6 → tiLC → hMhO → LIlk → TOfc → H8vo → nWXI → V0Δa → Δ4z2 → Βu94 → xkJ8 → pQdG → ZCrW → f2ΒQ → zEp6 → taTC → h6xO → rIlE → dSbS ⮌ | ||
| 58,325× | (max) 33 nodes | ⮎ 90Δw → ΔmH2 → ΒUZ4 → x4z8 → voFA → lYVK → R2Βe → zCr6 → tePC → hEpO → bIlU → T6xc → r8vE → ncRI → VAta → j4zM → vMhA → lKjK → ROfe → HCro → fWXQ → F0Δq → ΔaT2 → Β6x4 → xqD8 → pcRG → ZAtW → j2ΒM → zMh6 → tKjC → hOfO → JGnm → XSbY ⮌ | ||
| 58,261× | (max) 33 nodes | ⮎ B0Δu → ΔiL2 → ΒMh4 → xKj8 → pOfG → ZGnW → X2ΒY → z0Δ6 → ΔsB2 → ΒgN4 → xIl8 → pSbG → Z8vW → n2ΒI → zUZ6 → t4zC → vgNA → lIlK → TQdc → D8vs → nePI → VEpa → b4zU → v6xA → rkJE → dQdS → DAts → jePM → NEpi → bKjU → P6xg → rGnE → dWXS ⮌ | ||
| 57,893× | (max) 33 nodes | ⮎ 30ΔΓ → Δy52 → ΒsB4 → xgN8 → pIlG → ZSbW → 92Βw → zmH6 → tUZC → h4zO → vIlA → lSbK → R8ve → nCrI → fUZQ → F4zq → vaTA → l6xK → rQdE → dCrS → fAtQ → jEpM → bMhU → L6xk → rOfE → dGnS → XAtY → j0ΔM → ΔMh2 → ΒKj4 → xOf8 → pGnG → ZWXW ⮌ | ||
| 57,797× | (max) 33 nodes | ⮎ 94zw → vmHA → lUZK → R4ze → vCrA → lePK → REpe → bCrU → f6xQ → rEpE → daTS → B6xu → riLE → dMhS → LAtk → jOfM → NGni → XKjY → P0Δg → ΔGn2 → ΒWX4 → x0Δ8 → ΔoF2 → ΒYV4 → x2Β8 → zoF6 → tYVC → h2ΒO → zIl6 → tSbC → h8vO → nIlI → VSba ⮌ | ||
| 57,701× | (max) 33 nodes | ⮎ 96xw → rmHE → dUZS → B4zu → viLA → lMhK → RKje → PCrg → fGnQ → XEpY → b0ΔU → Δ6x2 → ΒqD4 → xcR8 → pAtG → jYVM → N2Βi → zKj6 → tOfC → hGnO → XIlY → T0Δc → Δ8v2 → ΒmH4 → xUZ8 → p4zG → vYVA → l2ΒK → zQd6 → tCrC → hePO → JEpm → bSbU ⮌ | ||
| 57,593× | (max) 33 nodes | ⮎ NKji → PKjg → PGng → XGnY → X0ΔY → Δ0Δ2 → ΔΑ32 → Βw74 → xoF8 → pYVG → Z2ΒW → z2Β6 → zsB6 → tgNC → hIlO → TIlc → T8vc → n8vI → nUZI → V4za → v4zA → vkJA → lQdK → RCre → fCrQ → fEpQ → bEpU → b6xU → r6xE → rcRE → dAtS → jAtM → jMhM ⮌ | ||
| 57,565× | (max) 33 nodes | ⮎ 70Δy → ΔqD2 → ΒcR4 → xAt8 → piLG → ZMhW → L2Βk → zOf6 → tGnC → hWXO → J0Δm → ΔSb2 → Β8v4 → xmH8 → pUZG → Z4zW → v2ΒA → zkJ6 → tQdC → hCrO → fIlQ → TEpc → b8vU → n6xI → rUZE → d4zS → vAtA → liLK → RMhe → LCrk → fOfQ → HEpo → bWXU ⮌ | ||
| 57,453× | (max) 33 nodes | ⮎ 50ΔΑ → Δu92 → ΒkJ4 → xQd8 → pCrG → fYVQ → F2Βq → zaT6 → t6xC → rgNE → dIlS → TAtc → j8vM → nMhI → VKja → P4zg → vGnA → lWXK → R0Δe → ΔCr2 → ΒeP4 → xEp8 → paTG → Z6xW → r2ΒE → zcR6 → tAtC → jgNM → NIli → TKjc → P8vg → nGnI → XUZY ⮌ | ||
| 57,149× | (max) 33 nodes | ⮎ 52ΒΑ → zu96 → tkJC → hQdO → JCrm → fSbQ → F8vq → naTI → V6xa → r4zE → vcRA → lAtK → jQdM → NCri → fKjQ → PEpg → bGnU → X6xY → r0ΔE → ΔcR2 → ΒAt4 → xiL8 → pMhG → ZKjW → P2Βg → zGn6 → tWXC → h0ΔO → ΔIl2 → ΒSb4 → x8v8 → pmHG → ZUZW ⮌ | ||
| 56,765× | (max) 33 nodes | ⮎ 74zy → vqDA → lcRK → RAte → jCrM → fMhQ → LEpk → bOfU → H6xo → rWXE → d0ΔS → ΔAt2 → ΒiL4 → xMh8 → pKjG → ZOfW → H2Βo → zWX6 → t0ΔC → ΔgN2 → ΒIl4 → xSb8 → p8vG → nYVI → V2Βa → z4z6 → vsBA → lgNK → RIle → TCrc → f8vQ → nEpI → bUZU ⮌ | ||
| 56,677× | (max) 33 nodes | ⮎ 72Βy → zqD6 → tcRC → hAtO → jIlM → TMhc → L8vk → nOfI → VGna → X4zY → v0ΔA → ΔkJ2 → ΒQd4 → xCr8 → pePG → ZEpW → b2ΒU → z6x6 → tqDC → hcRO → JAtm → jSbM → N8vi → nKjI → VOfa → H4zo → vWXA → l0ΔK → ΔQd2 → ΒCr4 → xeP8 → pEpG → bYVU ⮌ | ||
| 55,853× | (max) 33 nodes | ⮎ FAtq → jaTM → N6xi → rKjE → dOfS → HAto → jWXM → N0Δi → ΔKj2 → ΒOf4 → xGn8 → pWXG → Z0ΔW → Δ2Β2 → Βy54 → xsB8 → pgNG → ZIlW → T2Βc → z8v6 → tmHC → hUZO → J4zm → vSbA → l8vK → nQdI → VCra → f4zQ → vEpA → laTK → R6xe → rCrE → fcRQ ⮌ | ||
| 55,597× | (max) 33 nodes | ⮎ D4zs → vePA → lEpK → bQdU → D6xs → rePE → dEpS → bAtU → j6xM → rMhE → dKjS → PAtg → jGnM → XMhY → L0Δk → ΔOf2 → ΒGn4 → xWX8 → p0ΔG → ΔYV2 → Β2Β4 → zw76 → toFC → hYVO → J2Βm → zSb6 → t8vC → ngNI → VIla → T4zc → v8vA → nkJI → VQda ⮌ | ||
| 55,501× | (max) 33 nodes | ⮎ B2Βu → ziL6 → tMhC → hKjO → PIlg → TGnc → X8vY → n0ΔI → ΔUZ2 → Β4z4 → xu98 → pkJG → ZQdW → D2Βs → zeP6 → tEpC → haTO → J6xm → rSbE → d8vS → nAtI → jUZM → N4zi → vKjA → lOfK → RGne → XCrY → f0ΔQ → ΔEp2 → ΒaT4 → x6x8 → roFE → dYVS ⮌ | ||
| 5 | 2 cycles | 8,677,222× | 3 nodes | ⮎ iKΕjN → kLΕiL → jOΕfM ⮌ |
| 4,342,620× | (max) 4 nodes | ⮎ iLΕiN → jKΕjM → kMΕhL → jNΕgM ⮌ | ||
| 6 | 5 cycles | 100,252,147× | (max) 14 nodes | ⮎ ZRBsdW → hC2ΒsO → zgIlO6 → tTHmbC → hV7wZO → pJ3ΑlG → xZRcV8 → pB3ΑtG → xiYVM8 → pM2ΒiG → zZLiV6 → tN3ΑhC → xhJkN8 → pRJkdG ⮌ |
| 40,059,266× | (max) 14 nodes | ⮎ TJ9ulc → lS8vcK → nR9udI → lVBsZK → hR3ΑdO → xJBsl8 → phRcNG → ZKAtkW → jQ2ΒeM → zNDqh6 → tdJkRC → hRBsdO → hJBslO → hSIlcO ⮌ | ||
| 10,065,181× | 4 nodes | ⮎ pR3ΑdG → xZBsV8 → ph3ΑNG → xZJkV8 ⮌ | ||
| 5,147,540× | 10 nodes | ⮎ RL9uje → lOCrgK → fRHmdQ → VFBspa → ha4zUO → vJ5ylA → tlRcJC → hSAtcO → jJ9ulM → lSMhcK ⮌ | ||
| 714,707× | 6 nodes | ⮎ ZSAtcW → jA2ΒuM → zkMhK6 → tQKjeC → hPDqfO → dJFolS ⮌ | ||
| 7 | 1 cycle | 1,629,348,545× | (max) 8 nodes | ⮎ oXDΕqXH → rZGΕnVE → qbHΕmTF → pZIΕlVG → oXFΕoXH → pXGΕnXG → oZFΕoVH → pXIΕlXG ⮌ |
| 8 | 7 cycles | 7,960,311,496× | 14 nodes | ⮎ hREBsqdO → hcJBslSO → hSJ9ulcO → lSJ9ulcK → lSR9udcK → lRC9usdK → lgRBsdOK → hRIBsmdO → hUJBslaO → hSJ5ylcO → tSJ9ulcC → lhS9ucNK → lRK9ukdK → lRQBsedK ⮌ |
| 4,777,036,115× | 24 nodes | ⮎ dQJ3ΑleS → xSEAtqc8 → pjc9uSLG → lZO9ugVK → lRI3ΑmdK → xURBsda8 → phC5ysNG → tgZJkVOC → hRI3ΑmdO → xUJBsla8 → phS5ycNG → tZK9ukVC → lhQ3ΑeNK → xRKDqkd8 → pdQBseRG → hZEBsqVO → hcJ3ΑlSO → xSJ9ulc8 → plS9ucJG → lZS9ucVK → lRA3ΑudK → xkRBsdK8 → phQBseNG → hZKDqkVO ⮌ | ||
| 1,425,311,924× | 10 nodes | ⮎ pdA3ΑuRG → xkZBsVK8 → phQ3ΑeNG → xZKDqkV8 → pdQ3ΑeRG → xZEBsqV8 → phc3ΑSNG → xZK9ukV8 → plQ3ΑeJG → xZSDqcV8 ⮌ | ||
| 578,249,508× | 4 nodes | ⮎ pRM3ΑidG → xZMBsiV8 → phM3ΑiNG → xZMJkiV8 ⮌ | ||
| 159,904,008× | 19 nodes | ⮎ NJ63Αyli → xsSKjcC8 → pgP9ufOG → lZIFomVK → ZUR3ΑdaW → xC62Βys8 → zspfOFC6 → tgaGnUOC → hXI5ymXO → tUIΕΕlaC → smPAtfID → jfUFoaPM → ZNG5yohW → tYK2ΒkWC → zhQ1ΓeN6 → ΒtKDqkB4 → xidPeRM8 → pMFBspiG → haZLiVUO ⮌ | ||
| 123,053,715× | (max) 40 nodes | ⮎ RDA1Γure → ΒkeCrQK4 → xfQDqeP8 → pdGDqoRG → dZYBsWVS → hB41ΓΑtO → ΒwiIlM84 → xoTLibG8 → pYN7whWG → pZK1ΓkVG → ΒZQ3ΑeV4 → ywE3Αq87 → xrobSGD8 → peY8vWQG → nZE1ΓqVI → ΒcV3ΑZS4 → ywA3Αu87 → xrojKGD8 → peYOfWQG → ZHE1ΓqnW → ΒcW2ΒYS4 → zxA1Γu76 → ΒtqjKEB4 → xicOfSM8 → pMH9uniG → lZWLiYVK → RN41ΓΑhe → ΒwKCrk84 → xofPePG8 → pYGEpoWG → bZY1ΓWVU → Β741ΓΑx4 → ΒxwpE874 → xqoaTGE8 → pcY6xWSG → rZA1ΓuVE → Βkd3ΑRK4 → ywQBse87 → rohDqNGE → ecYJkWSR ⮌ | ||
| 47,607,828× | 10 nodes | ⮎ RLA9uuje → lkOCrgKK → fRQHmedQ → VFEBsqpa → hca4zUSO → vJA5yulA → tlkRcKJC → hSQAtecO → jJE9uqlM → lcSMhcSK ⮌ | ||
| 9+ | - | - | - | Not showing digit sets 9+ due to verbosity. |