Base 75: 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---
21 cycle 2,664×(max) 9 nodes⮎ 3Κ → Ζ7 → xF → hV → BΒ → pN → Rl → Jt → Zd ⮌
31 cycle 73,075×(max) 2 nodes⮎ aΝc → bΝb ⮌
444 cycles47,981×(max) 20 nodes⮎ RMpm → TKrk → XGvg → f8ΔY → v6ΖI → zcZE → l2ΚS → ΘIt6 → ΒabC → p0ΜO → ΜQl2 → ΚKr4 → ΖWf8 → x8ΔG → vgVI → dAΒa → r2ΚM → ΘUh6 → ΒCzC → pmPO ⮌
46,349×(max) 20 nodes⮎ HCzw → neXQ → N6Ζq → zSjE → lGvS → fItY → b6Ζc → z0ΜE → ΜkR2 → ΚIt4 → Ζab8 → x0ΜG → ΜgV2 → ΚAΒ4 → ΖqL8 → xUhG → hCzW → nAΒQ → rMpM → VSji ⮌
46,110×(max) 20 nodes⮎ F6Ζy → ziTE → lExS → jItU → bExc → j0ΜU → ΜEx2 → ΚiT4 → ΖEx8 → xiTG → hExW → jAΒU → rExM → jUhU → FCzy → niTQ → NExq → jSjU → HExw → jeXU ⮌
45,846×(max) 20 nodes⮎ 96ΖΕ → zuHE → lcZS → J2Κu → Θab6 → Β0ΜC → ΜoN2 → ΚQl4 → ΖKr8 → xWfG → h8ΔW → vAΒI → rcZM → V2Κi → ΘCz6 → ΒmPC → pMpO → TQlk → LGvs → fWfY ⮌
45,398×(max) 20 nodes⮎ 30ΜΛ → ΜΗ52 → ΚΑB4 → ΖoN8 → xQlG → hKrW → XAΒg → r8ΔM → vUhI → dCza → n2ΚQ → ΘMp6 → ΒSjC → pGvO → fQlY → L6Ζs → zWfE → l8ΔS → vItI → daba ⮌
44,790×(max) 20 nodes⮎ F0Μy → ΜiT2 → ΚEx4 → ΖiT8 → xExG → jgVU → FAΒy → riTM → VExi → jCzU → nExQ → jMpU → TExk → jGvU → fExY → j6ΖU → zExE → liTS → JExu → jabU ⮌
44,789×(max) 20 nodes⮎ JAΒu → rabM → V0Μi → ΜCz2 → ΚmP4 → ΖMp8 → xSjG → hGvW → fAΒY → r6ΖM → zUhE → lCzS → nItQ → bMpc → T0Μk → ΜGv2 → ΚeX4 → Ζ6Ζ8 → zwFE → lgVS ⮌
44,518×(max) 20 nodes⮎ B2ΚΓ → ΘqL6 → ΒUhC → pCzO → nQlQ → NKrq → XSjg → H8Δw → veXI → d6Ζa → z2ΚE → ΘkR6 → ΒItC → pabO → R0Μm → ΜKr2 → ΚWf4 → Ζ8Δ8 → xuHG → hcZW ⮌
44,422×(max) 20 nodes⮎ 52ΚΙ → ΘΓ96 → ΒsJC → pYdO → R4Θm → ΔKrA → tWfK → Z8Δe → v4ΘI → ΔcZA → t2ΚK → ΘYd6 → Β4ΘC → ΔoNA → tQlK → ZKre → X4Θg → Δ8ΔA → vsJI → dYda ⮌
43,766×(max) 20 nodes⮎ 94ΘΕ → ΔuHA → tcZK → Z2Κe → Θ4Θ6 → ΔΑBA → toNK → ZQle → L4Θs → ΔWfA → t8ΔK → vYdI → d4Θa → Δ2ΚA → ΘsJ6 → ΒYdC → p4ΘO → ΔQlA → tKrK → ZWfe ⮌
43,478×(max) 20 nodes⮎ D8ΔΑ → vmPI → dMpa → T2Κk → ΘGv6 → ΒeXC → p6ΖO → zQlE → lKrS → XItg → b8Δc → v0ΜI → ΜcZ2 → Κ2Κ4 → ΘΕ76 → ΒwFC → pgVO → RAΒm → rKrM → XUhg ⮌
43,110×(max) 20 nodes⮎ LCzs → nWfQ → N8Δq → vSjI → dGva → f2ΚY → Θ6Ζ6 → ΒyDC → pkRO → RItm → bKrc → X0Μg → Μ8Δ2 → ΚuH4 → ΖcZ8 → x2ΚG → ΘgV6 → ΒAΒC → roNM → VQli ⮌
43,061×(max) 20 nodes⮎ P0Μo → ΜOn2 → ΚOn4 → ΖOn8 → xOnG → hOnW → PAΒo → rOnM → VOni → PCzo → nOnQ → PMpo → TOnk → PGvo → fOnY → P6Ζo → zOnE → lOnS → PIto → bOnc ⮌
42,917×(max) 20 nodes⮎ 70ΜΗ → ΜyD2 → ΚkR4 → ΖIt8 → xabG → h0ΜW → ΜAΒ2 → ΚqL4 → ΖUh8 → xCzG → ngVQ → NAΒq → rSjM → VGvi → fCzY → n6ΖQ → zMpE → lSjS → JGvu → fabY ⮌
42,869×(max) 20 nodes⮎ DAΒΑ → rmPM → VMpi → TCzk → nGvQ → fMpY → T6Ζk → zGvE → leXS → J6Ζu → zabE → l0ΜS → ΜIt2 → Κab4 → Ζ0Μ8 → ΜwF2 → ΚgV4 → ΖAΒ8 → xqLG → hUhW ⮌
42,717×(max) 20 nodes⮎ 74ΘΗ → ΔyDA → tkRK → ZIte → b4Θc → Δ0ΜA → ΜsJ2 → ΚYd4 → Ζ4Θ8 → ΔwFA → tgVK → ZAΒe → r4ΘM → ΔUhA → tCzK → nYdQ → N4Θq → ΔSjA → tGvK → fYdY ⮌
42,597×(max) 20 nodes⮎ 50ΜΙ → ΜΓ92 → ΚsJ4 → ΖYd8 → x4ΘG → ΔgVA → tAΒK → rYdM → V4Θi → ΔCzA → tmPK → ZMpe → T4Θk → ΔGvA → teXK → Z6Ζe → z4ΘE → ΔkRA → tItK → bYdc ⮌
42,389×(max) 20 nodes⮎ B6ΖΓ → zqLE → lUhS → JCzu → nabQ → N0Μq → ΜSj2 → ΚGv4 → ΖeX8 → x6ΖG → zgVE → lAΒS → rItM → bUhc → D0ΜΑ → ΜmP2 → ΚMp4 → ΖSj8 → xGvG → heXW ⮌
42,077×(max) 20 nodes⮎ H0Μw → ΜeX2 → Κ6Ζ4 → ΖyD8 → xkRG → hItW → bAΒc → r0ΜM → ΜUh2 → ΚCz4 → ΖmP8 → xMpG → hSjW → HAΒw → reXM → V6Ζi → zCzE → nkRQ → NItq → bSjc ⮌
41,849×(max) 20 nodes⮎ TGvk → fGvY → f6ΖY → z6ΖE → zkRE → lItS → bItc → b0Μc → Μ0Μ2 → ΜΙ32 → ΚΕ74 → ΖwF8 → xgVG → hAΒW → rAΒM → rUhM → VCzi → nCzQ → nMpQ → TMpk ⮌
41,661×(max) 20 nodes⮎ D4ΘΑ → ΔmPA → tMpK → ZSje → H4Θw → ΔeXA → t6ΖK → zYdE → l4ΘS → ΔItA → tabK → Z0Μe → Μ4Θ2 → ΚΓ94 → ΖsJ8 → xYdG → h4ΘW → ΔAΒA → tqLK → ZUhe ⮌
41,541×(max) 20 nodes⮎ 90ΜΕ → ΜuH2 → ΚcZ4 → Ζ2Κ8 → ΘwF6 → ΒgVC → pAΒO → rQlM → VKri → XCzg → n8ΔQ → vMpI → dSja → H2Κw → ΘeX6 → Β6ΖC → zoNE → lQlS → LIts → bWfc ⮌
41,461×(max) 20 nodes⮎ B8ΔΓ → vqLI → dUha → D2ΚΑ → ΘmP6 → ΒMpC → pSjO → RGvm → fKrY → X6Ζg → z8ΔE → vkRI → dIta → b2Κc → Θ0Μ6 → ΜΑB2 → ΚoN4 → ΖQl8 → xKrG → hWfW ⮌
41,101×(max) 20 nodes⮎ 72ΚΗ → ΘyD6 → ΒkRC → pItO → bQlc → L0Μs → ΜWf2 → Κ8Δ4 → ΖuH8 → xcZG → h2ΚW → ΘAΒ6 → ΒqLC → pUhO → RCzm → nKrQ → XMpg → T8Δk → vGvI → fcZY ⮌
40,677×(max) 20 nodes⮎ B4ΘΓ → ΔqLA → tUhK → ZCze → n4ΘQ → ΔMpA → tSjK → ZGve → f4ΘY → Δ6ΖA → zsJE → lYdS → J4Θu → ΔabA → t0ΜK → ΜYd2 → Κ4Θ4 → ΖΓ98 → xsJG → hYdW ⮌
38,941×(max) 20 nodes⮎ J8Δu → vabI → d0Μa → Μ2Κ2 → ΚΗ54 → ΖΑB8 → xoNG → hQlW → LAΒs → rWfM → V8Δi → vCzI → ncZQ → N2Κq → ΘSj6 → ΒGvC → peXO → R6Ζm → zKrE → lWfS ⮌
38,412×(max) 20 nodes⮎ H6Ζw → zeXE → l6ΖS → zItE → labS → J0Μu → Μab2 → Κ0Μ4 → ΜΕ72 → ΚwF4 → ΖgV8 → xAΒG → rgVM → VAΒi → rCzM → nUhQ → NCzq → nSjQ → NGvq → fSjY ⮌
38,412×(max) 20 nodes⮎ B0ΜΓ → ΜqL2 → ΚUh4 → ΖCz8 → xmPG → hMpW → TAΒk → rGvM → fUhY → D6ΖΑ → zmPE → lMpS → TItk → bGvc → f0ΜY → Μ6Ζ2 → ΚyD4 → ΖkR8 → xItG → habW ⮌
23,059×10 nodes⮎ P2Κo → ΘOn6 → ΒOnC → pOnO → ROnm → PKro → XOng → P8Δo → vOnI → dOna ⮌
22,906×10 nodes⮎ VIti → bCzc → n0ΜQ → ΜMp2 → ΚSj4 → ΖGv8 → xeXG → h6ΖW → zAΒE → rkRM ⮌
21,678×10 nodes⮎ L8Δs → vWfI → d8Δa → v2ΚI → ΘcZ6 → Β2ΚC → ΘoN6 → ΒQlC → pKrO → XQlg ⮌
21,678×10 nodes⮎ R2Κm → ΘKr6 → ΒWfC → p8ΔO → vQlI → dKra → X2Κg → Θ8Δ6 → ΒuHC → pcZO ⮌
19,950×10 nodes⮎ F2Κy → ΘiT6 → ΒExC → piTO → RExm → jKrU → XExg → j8ΔU → vExI → jcZU ⮌
19,950×10 nodes⮎ F8Δy → viTI → dExa → j2ΚU → ΘEx6 → ΒiTC → pExO → jQlU → LExs → jWfU ⮌
19,902×10 nodes⮎ RKrm → XKrg → X8Δg → v8ΔI → vcZI → d2Κa → Θ2Κ6 → ΘΑB6 → ΒoNC → pQlO ⮌
19,902×10 nodes⮎ 92ΚΕ → ΘuH6 → ΒcZC → p2ΚO → ΘQl6 → ΒKrC → pWfO → R8Δm → vKrI → dWfa ⮌
9,951×5 nodes⮎ L2Κs → ΘWf6 → Β8ΔC → voNI → dQla ⮌
8,900×4 nodes⮎ ZExe → j4ΘU → ΔExA → tiTK ⮌
8,420×4 nodes⮎ P4Θo → ΔOnA → tOnK → ZOne ⮌
8,380×4 nodes⮎ Z4Θe → Δ4ΘA → ΔsJA → tYdK ⮌
7,420×4 nodes⮎ F4Θy → ΔiTA → tExK → jYdU ⮌
4,930×2 nodes⮎ t4ΘK → ΔYdA ⮌
3,730×2 nodes⮎ PExo → jOnU ⮌
2,355×(fixed) 1 node ⮎ jExU ⮌
51 cycle 22,537,440×(fixed) (max) 1 node ⮎ oOΝnP ⮌
62 cycles213,596,546×(max) 146 nodes⮎ 863ΙΗΖ → ΖΑwFC8 → xogVOG → hQAΒmW → rMAΒqM → rVTihM → VFBΑxi → piCzUO → nRDylQ → lNJspS → ZSItke → bI4Θuc → Δc0ΜaA → Μt1ΛJ2 → ΛΙZc43 → ΘΕ2Κ86 → ΘΒvGB6 → ΒqeXMC → pU6ΖiO → zRDylE → mkJsSR → ZLHure → dW4Θga → ΔA2ΚΓA → ΘtrKJ6 → ΒaWfcC → p91ΛΔO → ΚuQlI4 → ΖcKra8 → xX1ΛfG → Κh7ΕV4 → ΖxBΑF8 → xphUNG → hSCzkW → nIAΒuQ → rcMpaM → VT1Λji → ΚGCzw4 → ΖnfWP8 → xO8ΔoG → vhPmVI → dNBΑpa → pS2ΚkO → ΘRHul6 → ΒdJsZC → pZ3ΙdO → ΖR3Ιl8 → ΖxJsF8 → xiYdUG → hE4ΘyW → ΔkAΒSA → trHuLK → dZVgda → B42ΚΙΓ → ΘΕqL86 → ΒwUhGC → pgCzWO → nR9ΓlQ → tNJspK → aYRked → J62ΚΗu → ΘΑabC6 → Βo0ΜOC → ΜpPmN2 → ΚSMpk4 → ΖTHuj8 → xdFwZG → ig3ΙWV → ΖD9Γz8 → xtlQJG → haKrcW → XB1ΛΒg → Κq8ΔM4 → ΖvTiH8 → xeExYG → jh5ΗVU → ΒFBΑxC → qohUON → TQCzmk → nMGvqQ → fUMpiY → TE6Ζyk → zkGvSE → lfHuXS → dJ7Εta → xa2ΚcG → Θh1ΛV6 → ΚΒBΑB4 → ΖqoNM8 → xUQliG → hLDyrW → lWAΒgS → rJ9ΓtM → taUhcK → ZD1Λze → Κm4ΘQ4 → ΖΔLq98 → xuUhIG → hcCzaW → nB1ΛΒQ → ΚqMpM4 → ΖUSji8 → xHDyvG → lhdYVS → JC4ΘΑu → ΔoabOA → tQ0ΜmK → ΜZLqd2 → ΚV3Ιh4 → ΗΕBΑ87 → zwoNGE → lgQlWS → LJ9Γts → taWfcK → Z91ΛΔe → Κu4ΘI4 → ΖΔba98 → xu0ΜIG → ΜhbaV2 → ΚC0ΜΑ4 → ΜΖnO72 → ΚyOnE4 → ΖkOnS8 → xPHunG → hdNoZW → RB3ΙΒm → ΖqKrM8 → xXTifG → hF7ΕxW → xiAΒUG → rhDyVM → lVBΑhS → pJBΑtO → paQlcO → RL1Λrm → ΚWKrg4 → ΖX9Γf8 → xt7ΕJG → xhZcVG → hC2ΚΑW → ΘoAΒO6 → ΒrPmLC → pWMpgO → TR9Γlk → tKGvsK → fZXedY ⮌
86,903,579×52 nodes⮎ GE3Ιyx → ΖkgVS8 → xIAΒuG → rhbaVM → VC0ΜΑi → ΜoCzO2 → ΚnPmP4 → ΖOMpo8 → xTPmjG → hNFwpW → hSAΒkW → rIAΒuM → rcUhaM → VD1Λzi → ΚmCzQ4 → ΖnLqP8 → xVNohG → hRBΑlW → pKAΒsO → rYQleM → VL5Ηri → ΒWCzgC → pn9ΓPO → tRNolK → ZRJsle → ZK4Θse → ΔY4ΘeA → Δt5ΗJA → ΒtZcJC → pa2ΚcO → ΘR1Λl6 → ΚΒJsB4 → ΖqYdM8 → xU4ΘiG → ΔhDyVA → tlBΑRK → pZJsdO → ZR3Ιle → ΖK4Θs8 → ΔxXeFA → ti6ΖUK → zZDydE → mk3ΙSR → ΖLHur8 → xdVgZG → hB3ΙΒW → ΖqAΒM8 → xrTiLG → hWExgW → jB9ΓΒU → tqExMK → jZTidU ⮌
71 cycle 3,477,216,525×(max) 8 nodes⮎ ubFΝwbJ → xdIΝtZG → wfJΝsXH → vdKΝrZI → ubHΝubJ → vbIΝtbI → udHΝuZJ → vbKΝrbI ⮌
8+---Not showing digit sets 8+ due to verbosity.