Base 194: 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
стуфхцчшщъыьэюяァ
アィイゥウェエォオカガキギクグケ
ゲコゴサザシジスズセゼソゾタダチ

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 steps1 → 0 → 0
214 max steps20 → 1ゲ → グ3 → ガ7 → イF → уV → УΒ → ΕР → yЦ → ΛК → mв → λμ → 0コ → ゲ1 → グ3
399 max steps100 → 0ココ → ゲコ1 → ケコ2 → グコ3 → クコ4 → ギコ5 → キコ6 → ガコ7 → カコ8 → オコ9 → ォコA → エコB → ェコC → ウコD → ゥコE → イコF → ィコG → アコH → ァコI → яコJ → юコK → эコL → ьコM → ыコN → ъコO → щコP → шコQ → чコR → цコS → хコT → фコU → уコV → тコW → сコX → рコY → пコZ → оコa → нコb → мコc → лコd → кコe → йコf → иコg → зコh → жコi → еコj → дコk → гコl → вコm → бコn → аコo → Яコp → Юコq → Эコr → Ьコs → Ыコt → Ъコu → Щコv → Шコw → Чコx → Цコy → Хコz → ФコΑ → УコΒ → ТコΓ → СコΔ → РコΕ → ПコΖ → ОコΗ → НコΘ → МコΙ → ЛコΚ → КコΛ → ЙコΜ → ИコΝ → ЗコΞ → ЖコΟ → ЕコΠ → ДコΡ → ГコΣ → ВコΤ → БコΥ → АコΦ → ωコΧ → ψコΨ → χコΩ → φコα → υコβ → τコγ → σコδ → ςコε → ρコζ → πコη → οコθ → ξコι → νコκ → μコλ → λコμ → λコμ
431 max stepsO00Μ → ΜNъК → гlвm → ξλλκ → 3ココグ → グ2グ4 → ギカ76 → エィFC → ытVO → гТΒm → νΔРλ → Α1ケХ → グΘМ4 → ガrЬ8 → イΩφG → уLьW → зТΒi → υΔРγ → ΑHァХ → пΘМa → ЛrЬΛ → αnаχ → ιLьο → з5キi → エτβC → ыHァO → пвla → ЛμκΛ → o1ケб → グθξ4 → ガ5キ8 → エィFC
575 max stepsλ0000 → κコココν → νιコνλ → ξ1コケκ → ゲκコμ2 → ケλコλ3 → グιコν4 → クκコμ5 → ギθコξ6 → キιコν7 → ガηコο8 → カθコξ9 → オζコπA → ォηコοB → エεコρC → ェζコπD → ウδコςE → ゥεコρF → イγコσG → ィδコςH → アβコτI → ァγコσJ → яαコυK → юβコτL → эΩコφM → ьαコυN → ыΨコχO → ъΩコφP → щΧコψQ → шΨコχR → чΦコωS → цΧコψT → хΥコАU → фΦコωV → уΤコБW → тΥコАX → сΣコВY → рΤコБZ → пΡコГa → оΣコВb → нΠコДc → мΡコГd → лΟコЕe → кΠコДf → йΞコЖg → иΟコЕh → зΝコЗi → жΞコЖj → еΜコИk → дΝコЗl → гΛコЙm → вΜコИn → бΚコКo → аΛコЙp → ЯΙコЛq → ЮΚコКr → ЭΘコМs → ЬΙコЛt → ЫΗコНu → ЪΘコМv → ЩΖコОw → ШΗコНx → ЧΕコПy → ЦΖコОz → ХΔコРΑ → ФΕコПΒ → УΓコСΓ → ТΔコРΔ → СΒコТΕ → УΑコУΓ → ФΔコРΒ → УΔコРΓ → ТΓコСΔ → ТΒコТΔ → УΒコТΓ → УΔコРΓ