Base 91: Maximum Iteration Sequences: Full Cycle

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 Max Steps Max Step Example
Full Cycle
12 max steps100
215 max steps10 → 0ε → δ1 → β3 → Χ7ΞFxVZtpdΖNhlΧ7
348 max steps100 → 0εε → δε1 → γε2 → βε3 → αε4 → Ωε5 → Ψε6 → Χε7 → Φε8 → Υε9 → ΤεA → ΣεB → ΡεC → ΠεD → ΟεE → ΞεF → ΝεG → ΜεH → ΛεI → ΚεJ → ΙεK → ΘεL → ΗεM → ΖεN → ΕεO → ΔεP → ΓεQ → ΒεR → ΑεS → zεT → yεU → xεV → wεW → vεX → uεY → tεZ → sεa → rεb → qεc → pεd → oεe → nεf → mεg → lεh → kεi → jεjiεkjεj
416 max stepsk000 → jεεj → jijk → 1εεδ → δ0δ2δα32βΦ74ΧΝF8ΞwVGxQΒWbQΒsbGΜsvGΜYvMΖYjMΖkj0δkδ0δ2
539 max steps10000 → 0εεεε → δεεε1 → δ0εδ2 → εαε31 → δαε32 → γΩε43 → βΧε64 → αΤε95 → ΩΟεD6 → ΨΚεI7 → ΧΔεO8 → ΦwεV9 → ΥoεdA → ΤfεmB → ΣcεpC → ΡeεnD → ΠbεqE → ΟdεoF → ΞaεrG → ΝcεpH → ΜZεsI → ΛbεqJ → ΚYεtK → ΙaεrL → ΘXεuM → ΗZεsN → ΖWεvO → ΕYεtP → ΔVεwQ → ΓXεuR → ΒUεxS → ΑWεvT → zTεyU → zUεxU → yUεxV → ySεzVΑTεyTzWεvUySεzV
6330 max steps9000GΟ → ΟG8ΥΝF → ΜzvWTI → tWOΔwa → fQIΚΓo → rc8Υqc → ΜFDΟΞI → ΒysZUS → ZUIΚyu → rUKΘyc → nUEΞyg → zU6ΧyU → ΠVTyxE → ΒVRΑxS → aYRΑut → ZMIΚΗu → rkKΘic → nF1γΞg → βy6ΧU4 → ΧΠTyD8 → ΞΓUxQG → xcSzqW → XRDΟΒw → ΒaOΔsS → fZHΛto → tK8ΥΙa → ΜoIΚeI → tr9Τba → ΚJFΝΚK → xqodcW → REAΣΟΓ → ΘΑarSM → lYGΜui → vM2βΗY → ΩkMΖi6 → Σj1γjC → βΕεεN4 → αΖKΘN5 → ΥnhkfA → Κ82βΦK → ΩΝodG6 → ΣwAΣWC → ΘΖPΓNM → licpki → D31γβΡ → βΨΓP64 → ΧΡcpC8 → ΞΕCΠOG → ΔxfmVQ → dS6ΧΑq → ΠYCΠuE → ΔΒLΗRQ → ldZspi → JC2βΡΛ → ΩΕqbO6 → ΣgEΞmC → Ζz5ΨTO → ΣhVwlC → ΖR3αΒO → ΧhZsl8 → ΞJ3αΚG → ΧxpcV8 → ΞSCΠΑG → ΔxXuVQ → dSMΖΑq → jYCΠuk → ΔM0δΗQ → δkcpi2 → βD1γΠ4 → βΧΒQ74 → ΧΟarE8 → ΞΑGΜSG → xvXuXW → ROMΖΕΓ → jgarmk → H60δΨΝ → δΡuXC2 → βΕMΖO4 → Χjfmj8 → Ξ6εεΧG → ΨΝ7ΦG7 → ΠΞvWFE → ΒyOΔUS → fZTyto → VK8ΥΙy → ΜoSzeI → tX9Τva → ΚOIΚΕK → rpfmdc → FC6ΧΡΟ → ΠΕyTOE → ΒgUxmS → ZT5Ψzu → ΣWKΘwC → ΖnPΓfO → hd7Φpm → ΞC4ΩΡG → ΥΕwVOA → ΚgQΒmK → pb5Ψre → ΣGAΣΝC → ΘΖvWNM → liOΔki → f31γβo → βΨ8Υ64 → ΧΡΛHC8 → ΞΕsZOG → xgIΚmW → rR5ΨΒc → ΣaEΞsC → ΖzHΛTO → thVwla → RJ3αΚΓ → Χqarc8 → ΞHDΟΜG → ΒxtYVS → ZSKΘΑu → nYKΘug → nM6ΧΗg → Πk6ΧiE → ΠΒ1γRE → βΒZsR4 → ΧaIΚs8 → ΞrHΛbG → xtFΝZW → xRJΙΒW → paQΒse → bIAΣΛs → ΘsGΜaM → vlHΛhY → tN3αΖa → ΧiIΚk8 → Ξr1γbG → βxFΝV4 → ΧxRΑV8 → ΞZRΑtG → xZJΙtW → pRJΙΒe → paAΣse → ΘIAΣΛM → ΘskhaM → lI2βΛi → Ωs2βa6 → ΩΣHΛB6 → ΣΗsZMC → ΖkIΚiO → rh1γlc → βF3αΞ4 → ΨΦxU87 → ΠΝSzGE → ΒwWvWS → ZQOΔΓu → fcKΘqo → nE8ΥΟg → ΜΑ6ΧSI → ΠtXuZE → ΒNJΙΖS → piYtke → LB1γΣΙ → βΗmfM4 → Χk6Χi8 → ΠΞ1γFE → βΒxUR4 → ΧaSzs8 → ΞXHΛvG → xtNΕZW → hRJΙΒm → pa4Ωse → ΥIAΣΛA → ΚΘraLK → pmGΜge → vB5ΨΣY → ΣΗMΖMC → ΖkijiO → h20δγm → δα4Ω42 → βΦΤ984 → ΧΝΙJG8 → ΞwodWG → xQAΣΓW → ΘcQΒqM → lbDΟri → ΒG2βΝS → ΩwYtW6 → ΣQKΘΓC → ΖnbqfO → hF7ΦΞm → Ξy4ΩUG → ΥxTyVA → ΚVRΑxK → pZRΑte → ZKAΣΙu → ΘoKΘeM → nl9Τhg → Κ73αΧK → ΧΟodE8 → ΞΑAΣSG → ΘxXuVM → lSMΖΑi → jY2βuk → ΩM0δΗ6 → δΣjiB2 → βΗ0δM4 → δΧji72 → βΟ0δE4 → δΧzS72 → βΟWvE4 → ΧΑOΔS8 → ΞfXunG → xN7ΦΖW → ΞiQΒkG → xb1γrW → βRFΝΒ4ΧxZsV8ΞSIΚΑGxrXubWRNFΝΖΓxiarkWRH1γΜΓβuarY4ΧMGΜΗ8ΞvjiXGxO0δΕWδgQΒm2βb5Ψr4ΧΣFΝB8ΞΗwVMGxkQΒiWbR1γΒsβaGΜs4ΧvHΛX8ΞtNΕZGxhJΙlWpR3αΒeΧaAΣs8ΞΘHΛLGxtlgZWRK4ΩΙΓΥoareAΚH9ΤΜKΚuodYKpMAΣΗeΘkAΣiMΘl1γhMβl3αh4ΨΦ3α87ΧΠΜGD8ΞΓuXQGxcMΖqWjRDΟΒkΒa0δsSδZHΛt2βtJΙZ4ΧpJΙd8ΞpBΡdGΖxBΡVOΖhRΑlOhZ3αtmΧK4ΩΙ8ΥΞneFAΚy8ΥUKΜpTydItVBΡxaΖSIΚΑOrhXulcNF3αΞΗΧyijU8ΞU0δyGδxTyV2βVRΑx4ΧZRΑt8ΞZJΙtGxpJΙdWpRBΡΒeΖaAΣsOΘhHΛlMtl3αhaΧJ3αΚ8ΧΞpcF8ΞyCΠUGΔxTyVQdVRΑxqZSCΠΑuΔYKΘuQndLΗpglC6ΧΡiΠΕ2βOEΩΒfmR6Σa6ΧsCΠΖHΛNEΒthkZSZK2βΙuΩoKΘe6Σn9ΤfCΚΖ7ΦNKΞphkdGxC2βΡWΩΕQΒO6ΣgarmCΖH5ΨΜOΣuglYCΖM4ΩΗOΥkgliAΚ51γΩKβΤodA4ΧΙAΣK8ΞΘneLGxm8ΥgWΜR5ΨΒIΣtZsZCΖKIΚΙOroglecFA4ΩΤΟΥΙyTKAΚoUxeKpT9ΤzeΚWAΣwKΘpPΓdMldBΡpiΖC2βΡOΩΕglO6Σg4ΩmCΥΖ5ΨNAΣΚhkJCΖq2βcOΩhDΟl6ΣΒ3αRCΧΖZsN8ΞiIΚkGxr1γbWβRFΝΒ4
756 max stepsC00000j → jBεεεΡk → ΣjhεkjC → Ρa0εδsD → εΟfεmE1 → δΟYεtE2 → γΞfεmF3 → βΜXεuH4 → αΙdεoK5 → ΩΕUεxO6 → ΨzZεsT7 → ΧtPεΓZ8 → ΦwSεzW9 → ΥsSεzaA → ΤrOεΔbB → ΣuRεΑYC → ΡqRεΑcD → ΠpNεΕdE → ΟsQεΒaF → ΞoQεΒeG → ΝnMεΖfH → ΜqPεΓcI → ΛmPεΓgJ → ΚlLεΗhK → ΙoOεΔeL → ΘkOεΔiM → ΗjKεΘjN → ΙkMεΖiL → ΘmMεΖgM → ΗlOεΔhN → ΖiLεΗkO → ΘiMεΖkM → ΗlMεΖhN → ΗjNεΕjN → ΖjKεΘjO → ΙjLεΗjL → ΘnMεΖfM → ΗlPεΓhN → ΖhKεΘlO → ΙjNεΕjL → ΘlKεΘhM → ΙlPεΓhL → ΘjKεΘjM → ΙlNεΕhL → ΘlMεΖhM → ΗlNεΕhN → ΖjMεΖjO → ΗhLεΗlN → ΘjOεΔjMΗjJεΙjNΚlMεΖhKΙnNεΕfLΘlOεΔhMΗjLεΗjNΘjMεΖjMΗlLεΗhNΘjOεΔjM