Base 75: Cycles Sequences: Maximum Length Cycle Count

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)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
21 cycle 9 nodes3Κ → Ζ7 → xF → hV → BΒ → pN → Rl → Jt → Zd
31 cycle 2 nodesaΝc → bΝb
444 cycles20 nodesB0ΜΓ → ΜqL2 → ΚUh4 → ΖCz8 → xmPG → hMpW → TAΒk → rGvM → fUhY → D6ΖΑ → zmPE → lMpS → TItk → bGvc → f0ΜY → Μ6Ζ2 → ΚyD4 → ΖkR8 → xItG → habW
51 cycle (fixed) 1 node oOΝnP
62 cycles146 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
71 cycle 8 nodesubFΝwbJ → xdIΝtZG → wfJΝsXH → vdKΝrZI → ubHΝubJ → vbIΝtbI → udHΝuZJ → vbKΝrbI