Base 123: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
23 cycles5 nodesJς → Χd → hΣ → Zβ → pΚ
31 cycle 2 nodesyЛΑ → zЛz
4104 cycles20 nodesB4ЖБ → ВοLA → ςΡhK → ΧYβe → rgΣΙ → bGτα → δmΜY → tOμΗ → ΜCψo → μMξQ → ΠΙpk → VIςη → Ωyzc → l0КΟ → КSθ2 → ИΓv4 → Д6Д8 → ψυFE → κεVS → ΖwΒu
51 cycle (fixed) 1 node ΦeЛΥf
67 cycles34 nodesrY4ЖγΙ → ВsGτΗA → ςδDχXK → κΧtΕdS → ΖiAАΡu → πYAАγM → πΣrΗhM → ΣaEφαi → θoYβΛU → ΒrLοΘy → ΣG2Иυi → ЖεYβW6 → АwqΘΓC → ξH5ЕτO → АγΝlYC → ξsQκΗO → ΞΘDχrm → κRFυκS → ζΗΕtsW → xEAАχΓ → πι4ЖSM → ВΣΔuhA → ςa8ВαK → τΧnΛdI → βiMξΡa → ΠpXγΚk → tVJρζΗ → ΧyCψΑe → μh1ЙΣQ → ИΚZαp4 → ДpJρΚ8 → φΧJρdG → ζΧhΡdW → xiYβΡΓ