Base 91: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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 11 nodes3β → Χ7 → ΞF → xV → RΒ → Zt → JΚ → pd → BΣ → ΖN → hl
31 cycle 2 nodesiεk → jεj
488 cycles12 nodesB0δΤ → δΗL2 → βkh4 → Χ2β8 → ΩΝF6 → ΣwVC → ΖQΒO → harm → H4ΩΝ → ΥuXA → ΚMΖK → pije
52 cycles4 nodesyTεyV → zSεzU → ΑUεxT → zVεwU
63 cycles118 nodesFA4ΩΤΟ → ΥΙyTKA → ΚoUxeK → pT9Τze → ΚWAΣwK → ΘpPΓdM → ldBΡpi → ΖC2βΡO → ΩΕglO6 → Σg4ΩmC → ΥΖ5ΨNA → ΣΚhkJC → Ζq2βcO → ΩhDΟl6 → ΣΒ3αRC → ΧΖZsN8 → ΞiIΚkG → xr1γbW → βRFΝΒ4 → ΧxZsV8 → ΞSIΚΑG → xrXubW → RNFΝΖΓ → xiarkW → RH1γΜΓ → βuarY4 → ΧMGΜΗ8 → ΞvjiXG → xO0δΕW → δgQΒm2 → βb5Ψr4 → ΧΣFΝB8 → ΞΗwVMG → xkQΒiW → bR1γΒs → βaGΜs4 → ΧvHΛX8 → ΞtNΕZG → xhJΙlW → pR3αΒe → ΧaAΣs8 → ΞΘHΛLG → xtlgZW → RK4ΩΙΓ → ΥoareA → ΚH9ΤΜK → ΚuodYK → pMAΣΗe → ΘkAΣiM → Θl1γhM → βl3αh4 → ΨΦ3α87 → ΧΠΜGD8 → ΞΓuXQG → xcMΖqW → jRDΟΒk → Βa0δsS → δZHΛt2 → βtJΙZ4 → ΧpJΙd8 → ΞpBΡdG → ΖxBΡVO → ΖhRΑlO → hZ3αtm → ΧK4ΩΙ8 → ΥΞneFA → Κy8ΥUK → ΜpTydI → tVBΡxa → ΖSIΚΑO → rhXulc → NF3αΞΗ → ΧyijU8 → ΞU0δyG → δxTyV2 → βVRΑx4 → ΧZRΑt8 → ΞZJΙtG → xpJΙdW → pRBΡΒe → ΖaAΣsO → ΘhHΛlM → tl3αha → ΧJ3αΚ8 → ΧΞpcF8 → ΞyCΠUG → ΔxTyVQ → dVRΑxq → ZSCΠΑu → ΔYKΘuQ → ndLΗpg → lC6ΧΡi → ΠΕ2βOE → ΩΒfmR6 → Σa6ΧsC → ΠΖHΛNE → ΒthkZS → ZK2βΙu → ΩoKΘe6 → Σn9ΤfC → ΚΖ7ΦNK → ΞphkdG → xC2βΡW → ΩΕQΒO6 → ΣgarmC → ΖH5ΨΜO → ΣuglYC → ΖM4ΩΗO → ΥkgliA → Κ51γΩK → βΤodA4 → ΧΙAΣK8 → ΞΘneLG → xm8ΥgW → ΜR5ΨΒI → ΣtZsZC → ΖKIΚΙO → roglec
71 cycle 8 nodesΗjJεΙjN → ΚlMεΖhK → ΙnNεΕfL → ΘlOεΔhM → ΗjLεΗjN → ΘjMεΖjM → ΗlLεΗhN → ΘjOεΔjM