Base 151: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа
бвгдежзийклмнопр

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
214 max steps10 → 0з → ж1 → д3 → а7 → ШFИVβΒςlΚΣШF
378 max steps100 → 0зз → жз1 → ез2 → дз3 → гз4 → вз5 → бз6 → аз7 → Яз8 → Юз9 → ЭзA → ЬзB → ЫзC → ЪзD → ЩзE → ШзF → ЧзG → ЦзH → ХзI → ФзJ → УзK → ТзL → СзM → РзN → ПзO → ОзP → НзQ → МзR → ЛзS → КзT → ЙзU → ИзV → ЗзW → ЖзX → ЕзY → ДзZ → Гзa → Взb → Бзc → Азd → ωзe → ψзf → χзg → φзh → υзi → τзj → σзk → ςзl → ρзm → πзn → οзo → ξзp → νзq → μзr → λзs → κзt → ιзu → θзv → ηзw → ζзx → εзy → δзz → γзΑ → βзΒ → αзΓ → ΩзΔ → ΨзΕ → ΧзΖ → ΦзΗ → ΥзΘ → ΤзΙ → ΣзΚ → ΡзΛ → ΠзΜ → ΟзΝ → ΞзΞΝзΟΞзΞ
419 max stepsΟ000 → ΞззΞ → ΞΝΞΟ → 1ззж → ж0ж2жг32дЯ74аЧF8ШЗVGИαΒWβMРΓτMРkτwζkxWЖηΩWЖΕΩIФΕВIФcВΝΞcΞ0жΟж0ж2
560 max steps1000I → I0зжЦ → зУзJ1 → жУзJ2 → еТзK3 → дРзM4 → гНзP5 → вЙзT6 → бДзY7 → аψзe8 → Яρзl9 → ЮιзtA → ЭΩзΓB → ЬΞзΝC → ЫΓзΩD → ЪΜзΟE → ЩΒзαF → ШΛзΠG → ЧΑзβH → ЦΚзΡI → ХzзγJ → ФΙзΣK → УyзδL → ТΘзΤM → СxзεN → РΗзΥO → ПwзζP → ОΖзΦQ → НvзηR → МΕзΧS → ЛuзθT → КΔзΨU → ЙtзιV → ИΓзΩW → ЗsзκX → ЖΒзαY → ЕrзλZ → ДΑзβa → Гqзμb → Вzзγc → Бpзνd → Аyзδe → ωoзξf → ψxзεg → χnзοh → φwзζi → υmзπj → τvзηk → σlзρl → ςuзθm → ρkзςn → σrзλl → ςoзξm → ρqзμn → πnзοo → πoзξo → οoзξp → οmзπpρnзοnπqзμoοmзπp