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 nodes3Κ → Ζ7 → xF → hV → BΒ → pN → Rl → Jt → Zd
31 cycle 73,075×(max) 2 nodesaΝc → bΝb
444 cycles47,981×(max) 20 nodesRMpm → TKrk → XGvg → f8ΔY → v6ΖI → zcZE → l2ΚS → ΘIt6 → ΒabC → p0ΜO → ΜQl2 → ΚKr4 → ΖWf8 → x8ΔG → vgVI → dAΒa → r2ΚM → ΘUh6 → ΒCzC → pmPO
46,349×(max) 20 nodesHCzw → neXQ → N6Ζq → zSjE → lGvS → fItY → b6Ζc → z0ΜE → ΜkR2 → ΚIt4 → Ζab8 → x0ΜG → ΜgV2 → ΚAΒ4 → ΖqL8 → xUhG → hCzW → nAΒQ → rMpM → VSji
46,110×(max) 20 nodesF6Ζy → ziTE → lExS → jItU → bExc → j0ΜU → ΜEx2 → ΚiT4 → ΖEx8 → xiTG → hExW → jAΒU → rExM → jUhU → FCzy → niTQ → NExq → jSjU → HExw → jeXU
45,846×(max) 20 nodes96ΖΕ → zuHE → lcZS → J2Κu → Θab6 → Β0ΜC → ΜoN2 → ΚQl4 → ΖKr8 → xWfG → h8ΔW → vAΒI → rcZM → V2Κi → ΘCz6 → ΒmPC → pMpO → TQlk → LGvs → fWfY
45,398×(max) 20 nodes30ΜΛ → ΜΗ52 → ΚΑB4 → ΖoN8 → xQlG → hKrW → XAΒg → r8ΔM → vUhI → dCza → n2ΚQ → ΘMp6 → ΒSjC → pGvO → fQlY → L6Ζs → zWfE → l8ΔS → vItI → daba
44,790×(max) 20 nodesF0Μy → ΜiT2 → ΚEx4 → ΖiT8 → xExG → jgVU → FAΒy → riTM → VExi → jCzU → nExQ → jMpU → TExk → jGvU → fExY → j6ΖU → zExE → liTS → JExu → jabU
44,789×(max) 20 nodesJAΒu → rabM → V0Μi → ΜCz2 → ΚmP4 → ΖMp8 → xSjG → hGvW → fAΒY → r6ΖM → zUhE → lCzS → nItQ → bMpc → T0Μk → ΜGv2 → ΚeX4 → Ζ6Ζ8 → zwFE → lgVS
44,518×(max) 20 nodesB2ΚΓ → ΘqL6 → ΒUhC → pCzO → nQlQ → NKrq → XSjg → H8Δw → veXI → d6Ζa → z2ΚE → ΘkR6 → ΒItC → pabO → R0Μm → ΜKr2 → ΚWf4 → Ζ8Δ8 → xuHG → hcZW
44,422×(max) 20 nodes52ΚΙ → ΘΓ96 → ΒsJC → pYdO → R4Θm → ΔKrA → tWfK → Z8Δe → v4ΘI → ΔcZA → t2ΚK → ΘYd6 → Β4ΘC → ΔoNA → tQlK → ZKre → X4Θg → Δ8ΔA → vsJI → dYda
43,766×(max) 20 nodes94ΘΕ → ΔuHA → tcZK → Z2Κe → Θ4Θ6 → ΔΑBA → toNK → ZQle → L4Θs → ΔWfA → t8ΔK → vYdI → d4Θa → Δ2ΚA → ΘsJ6 → ΒYdC → p4ΘO → ΔQlA → tKrK → ZWfe
43,478×(max) 20 nodesD8ΔΑ → vmPI → dMpa → T2Κk → ΘGv6 → ΒeXC → p6ΖO → zQlE → lKrS → XItg → b8Δc → v0ΜI → ΜcZ2 → Κ2Κ4 → ΘΕ76 → ΒwFC → pgVO → RAΒm → rKrM → XUhg
43,110×(max) 20 nodesLCzs → nWfQ → N8Δq → vSjI → dGva → f2ΚY → Θ6Ζ6 → ΒyDC → pkRO → RItm → bKrc → X0Μg → Μ8Δ2 → ΚuH4 → ΖcZ8 → x2ΚG → ΘgV6 → ΒAΒC → roNM → VQli
43,061×(max) 20 nodesP0Μo → ΜOn2 → ΚOn4 → ΖOn8 → xOnG → hOnW → PAΒo → rOnM → VOni → PCzo → nOnQ → PMpo → TOnk → PGvo → fOnY → P6Ζo → zOnE → lOnS → PIto → bOnc
42,917×(max) 20 nodes70ΜΗ → ΜyD2 → ΚkR4 → ΖIt8 → xabG → h0ΜW → ΜAΒ2 → ΚqL4 → ΖUh8 → xCzG → ngVQ → NAΒq → rSjM → VGvi → fCzY → n6ΖQ → zMpE → lSjS → JGvu → fabY
42,869×(max) 20 nodesDAΒΑ → rmPM → VMpi → TCzk → nGvQ → fMpY → T6Ζk → zGvE → leXS → J6Ζu → zabE → l0ΜS → ΜIt2 → Κab4 → Ζ0Μ8 → ΜwF2 → ΚgV4 → ΖAΒ8 → xqLG → hUhW
42,717×(max) 20 nodes74ΘΗ → ΔyDA → tkRK → ZIte → b4Θc → Δ0ΜA → ΜsJ2 → ΚYd4 → Ζ4Θ8 → ΔwFA → tgVK → ZAΒe → r4ΘM → ΔUhA → tCzK → nYdQ → N4Θq → ΔSjA → tGvK → fYdY
42,597×(max) 20 nodes50ΜΙ → ΜΓ92 → ΚsJ4 → ΖYd8 → x4ΘG → ΔgVA → tAΒK → rYdM → V4Θi → ΔCzA → tmPK → ZMpe → T4Θk → ΔGvA → teXK → Z6Ζe → z4ΘE → ΔkRA → tItK → bYdc
42,389×(max) 20 nodesB6ΖΓ → zqLE → lUhS → JCzu → nabQ → N0Μq → ΜSj2 → ΚGv4 → ΖeX8 → x6ΖG → zgVE → lAΒS → rItM → bUhc → D0ΜΑ → ΜmP2 → ΚMp4 → ΖSj8 → xGvG → heXW
42,077×(max) 20 nodesH0Μw → ΜeX2 → Κ6Ζ4 → ΖyD8 → xkRG → hItW → bAΒc → r0ΜM → ΜUh2 → ΚCz4 → ΖmP8 → xMpG → hSjW → HAΒw → reXM → V6Ζi → zCzE → nkRQ → NItq → bSjc
41,849×(max) 20 nodesTGvk → fGvY → f6ΖY → z6ΖE → zkRE → lItS → bItc → b0Μc → Μ0Μ2 → ΜΙ32 → ΚΕ74 → ΖwF8 → xgVG → hAΒW → rAΒM → rUhM → VCzi → nCzQ → nMpQ → TMpk
41,661×(max) 20 nodesD4ΘΑ → ΔmPA → tMpK → ZSje → H4Θw → ΔeXA → t6ΖK → zYdE → l4ΘS → ΔItA → tabK → Z0Μe → Μ4Θ2 → ΚΓ94 → ΖsJ8 → xYdG → h4ΘW → ΔAΒA → tqLK → ZUhe
41,541×(max) 20 nodes90ΜΕ → ΜuH2 → ΚcZ4 → Ζ2Κ8 → ΘwF6 → ΒgVC → pAΒO → rQlM → VKri → XCzg → n8ΔQ → vMpI → dSja → H2Κw → ΘeX6 → Β6ΖC → zoNE → lQlS → LIts → bWfc
41,461×(max) 20 nodesB8ΔΓ → vqLI → dUha → D2ΚΑ → ΘmP6 → ΒMpC → pSjO → RGvm → fKrY → X6Ζg → z8ΔE → vkRI → dIta → b2Κc → Θ0Μ6 → ΜΑB2 → ΚoN4 → ΖQl8 → xKrG → hWfW
41,101×(max) 20 nodes72ΚΗ → ΘyD6 → ΒkRC → pItO → bQlc → L0Μs → ΜWf2 → Κ8Δ4 → ΖuH8 → xcZG → h2ΚW → ΘAΒ6 → ΒqLC → pUhO → RCzm → nKrQ → XMpg → T8Δk → vGvI → fcZY
40,677×(max) 20 nodesB4ΘΓ → ΔqLA → tUhK → ZCze → n4ΘQ → ΔMpA → tSjK → ZGve → f4ΘY → Δ6ΖA → zsJE → lYdS → J4Θu → ΔabA → t0ΜK → ΜYd2 → Κ4Θ4 → ΖΓ98 → xsJG → hYdW
38,941×(max) 20 nodesJ8Δu → vabI → d0Μa → Μ2Κ2 → ΚΗ54 → ΖΑB8 → xoNG → hQlW → LAΒs → rWfM → V8Δi → vCzI → ncZQ → N2Κq → ΘSj6 → ΒGvC → peXO → R6Ζm → zKrE → lWfS
38,412×(max) 20 nodesH6Ζw → zeXE → l6ΖS → zItE → labS → J0Μu → Μab2 → Κ0Μ4 → ΜΕ72 → ΚwF4 → ΖgV8 → xAΒG → rgVM → VAΒi → rCzM → nUhQ → NCzq → nSjQ → NGvq → fSjY
38,412×(max) 20 nodesB0ΜΓ → ΜqL2 → ΚUh4 → ΖCz8 → xmPG → hMpW → TAΒk → rGvM → fUhY → D6ΖΑ → zmPE → lMpS → TItk → bGvc → f0ΜY → Μ6Ζ2 → ΚyD4 → ΖkR8 → xItG → habW
23,059×10 nodesP2Κo → ΘOn6 → ΒOnC → pOnO → ROnm → PKro → XOng → P8Δo → vOnI → dOna
22,906×10 nodesVIti → bCzc → n0ΜQ → ΜMp2 → ΚSj4 → ΖGv8 → xeXG → h6ΖW → zAΒE → rkRM
21,678×10 nodesL8Δs → vWfI → d8Δa → v2ΚI → ΘcZ6 → Β2ΚC → ΘoN6 → ΒQlC → pKrO → XQlg
21,678×10 nodesR2Κm → ΘKr6 → ΒWfC → p8ΔO → vQlI → dKra → X2Κg → Θ8Δ6 → ΒuHC → pcZO
19,950×10 nodesF2Κy → ΘiT6 → ΒExC → piTO → RExm → jKrU → XExg → j8ΔU → vExI → jcZU
19,950×10 nodesF8Δy → viTI → dExa → j2ΚU → ΘEx6 → ΒiTC → pExO → jQlU → LExs → jWfU
19,902×10 nodesRKrm → XKrg → X8Δg → v8ΔI → vcZI → d2Κa → Θ2Κ6 → ΘΑB6 → ΒoNC → pQlO
19,902×10 nodes92ΚΕ → ΘuH6 → ΒcZC → p2ΚO → ΘQl6 → ΒKrC → pWfO → R8Δm → vKrI → dWfa
9,951×5 nodesL2Κs → ΘWf6 → Β8ΔC → voNI → dQla
8,900×4 nodesZExe → j4ΘU → ΔExA → tiTK
8,420×4 nodesP4Θo → ΔOnA → tOnK → ZOne
8,380×4 nodesZ4Θe → Δ4ΘA → ΔsJA → tYdK
7,420×4 nodesF4Θy → ΔiTA → tExK → jYdU
4,930×2 nodest4ΘK → ΔYdA
3,730×2 nodesPExo → jOnU
2,355×(fixed) 1 node jExU
51 cycle 22,537,440×(fixed) (max) 1 node oOΝnP
62 cycles213,596,546×(max) 146 nodes863ΙΗΖ → 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 nodesGE3Ιyx → 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 nodesubFΝwbJ → xdIΝtZG → wfJΝsXH → vdKΝrZI → ubHΝubJ → vbIΝtbI → udHΝuZJ → vbKΝrbI
8+---Not showing digit sets 8+ due to verbosity.