Base 67: Cycles Sequences: All Cycle Counts

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits # Full Cycles
(excluding zero)
Frequency Cycle
Length
Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
22 cycles1,056×(max) 4 nodes3Β → x7 → pF → ZV
1,056×(max) 4 nodesBt → hN → Jl → Rd
31 cycle 52,327×(max) 2 nodesWΕY → XΕX
416 cycles58,349×(max) 33 nodesF6xq → 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 nodesB8vu → 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 nodes90Δw → 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 nodesB0Δu → 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 nodes30ΔΓ → 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 nodes94zw → 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 nodes96xw → 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 nodesNKji → 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 nodes70Δy → 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 nodes50ΔΑ → 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 nodes52ΒΑ → 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 nodes74zy → 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 nodes72Βy → 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 nodesFAtq → 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 nodesD4zs → 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 nodesB2Βu → 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
52 cycles8,677,222×3 nodesiKΕjN → kLΕiL → jOΕfM
4,342,620×(max) 4 nodesiLΕiN → jKΕjM → kMΕhL → jNΕgM
65 cycles100,252,147×(max) 14 nodesZRBsdW → hC2ΒsO → zgIlO6 → tTHmbC → hV7wZO → pJ3ΑlG → xZRcV8 → pB3ΑtG → xiYVM8 → pM2ΒiG → zZLiV6 → tN3ΑhC → xhJkN8 → pRJkdG
40,059,266×(max) 14 nodesTJ9ulc → lS8vcK → nR9udI → lVBsZK → hR3ΑdO → xJBsl8 → phRcNG → ZKAtkW → jQ2ΒeM → zNDqh6 → tdJkRC → hRBsdO → hJBslO → hSIlcO
10,065,181×4 nodespR3ΑdG → xZBsV8 → ph3ΑNG → xZJkV8
5,147,540×10 nodesRL9uje → lOCrgK → fRHmdQ → VFBspa → ha4zUO → vJ5ylA → tlRcJC → hSAtcO → jJ9ulM → lSMhcK
714,707×6 nodesZSAtcW → jA2ΒuM → zkMhK6 → tQKjeC → hPDqfO → dJFolS
71 cycle 1,629,348,545×(max) 8 nodesoXDΕqXH → rZGΕnVE → qbHΕmTF → pZIΕlVG → oXFΕoXH → pXGΕnXG → oZFΕoVH → pXIΕlXG
87 cycles7,960,311,496×14 nodeshREBsqdO → hcJBslSO → hSJ9ulcO → lSJ9ulcK → lSR9udcK → lRC9usdK → lgRBsdOK → hRIBsmdO → hUJBslaO → hSJ5ylcO → tSJ9ulcC → lhS9ucNK → lRK9ukdK → lRQBsedK
4,777,036,115×24 nodesdQJ3ΑleS → 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 nodespdA3ΑuRG → xkZBsVK8 → phQ3ΑeNG → xZKDqkV8 → pdQ3ΑeRG → xZEBsqV8 → phc3ΑSNG → xZK9ukV8 → plQ3ΑeJG → xZSDqcV8
578,249,508×4 nodespRM3ΑidG → xZMBsiV8 → phM3ΑiNG → xZMJkiV8
159,904,008×19 nodesNJ63Αyli → xsSKjcC8 → pgP9ufOG → lZIFomVK → ZUR3ΑdaW → xC62Βys8 → zspfOFC6 → tgaGnUOC → hXI5ymXO → tUIΕΕlaC → smPAtfID → jfUFoaPM → ZNG5yohW → tYK2ΒkWC → zhQ1ΓeN6 → ΒtKDqkB4 → xidPeRM8 → pMFBspiG → haZLiVUO
123,053,715×(max) 40 nodesRDA1Γure → 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 nodesRLA9uuje → lkOCrgKK → fRQHmedQ → VFEBsqpa → hca4zUSO → vJA5yulA → tlkRcKJC → hSQAtecO → jJE9uqlM → lcSMhcSK
9+---Not showing digit sets 9+ due to verbosity.