Base 147: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
24 max steps10 → 0г → в1 → а3 → Ь7
374 max steps100 → 0гг → вг1 → бг2 → аг3 → Яг4 → Юг5 → Эг6 → Ьг7 → Ыг8 → Ъг9 → ЩгA → ШгB → ЧгC → ЦгD → ХгE → ФгF → УгG → ТгH → СгI → РгJ → ПгK → ОгL → НгM → МгN → ЛгO → КгP → ЙгQ → ИгR → ЗгS → ЖгT → ЕгU → ДгV → ГгW → ВгX → БгY → АгZ → ωгa → ψгb → χгc → φгd → υгe → τгf → σгg → ςгh → ρгi → πгj → οгk → ξгl → νгm → μгn → λгo → κгp → ιгq → θгr → ηгs → ζгt → εгu → δгv → γгw → βгx → αгy → Ωгz → ΨгΑ → ΧгΒ → ΦгΓ → ΥгΔ → ΤгΕ → ΣгΖ → ΡгΗ → ΠгΘ → ΟгΙ → ΞгΚ → ΝгΛ → ΜгΜ
44 max stepsΝ000 → ΜггΜ → ΜΛΜΝ → 1ггв → в0в2
558 max steps1000G → G0гвФ → гСгH1 → вСгH2 → бРгI3 → аОгK4 → ЯЛгN5 → ЮЗгR6 → ЭВгW7 → Ьφгc8 → Ыοгj9 → ЪηгrA → ЩΧгΑB → ШΜгΛC → ЧΑгΧD → ЦΚгΝE → ХzгΨF → ФΙгΞG → УyгΩH → ТΘгΟI → СxгαJ → РΗгΠK → ПwгβL → ОΖгΡM → НvгγN → МΕгΣO → ЛuгδP → КΔгΤQ → ЙtгεR → ИΓгΥS → ЗsгζT → ЖΒгΦU → ЕrгηV → ДΑгΧW → ГqгθX → ВzгΨY → БpгιZ → АyгΩa → ωoгκb → ψxгαc → χnгλd → φwгβe → υmгμf → τvгγg → σlгνh → ςuгδi → ρkгξj → πtгεk → οjгοl → πqгθk → οmгμl → ξpгιm → νlгνn → ξmгμm → νoгκn → μlгνo → ξlгνm → ξoгκm → νmгμn