Base 153: 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
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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
23 cycles30 nodes1и → ж3 → в7 → ЪF → КV → δΒ → PР → πp → nς → rξ → jφ → zζ → TМ → θx → XИ → ΩΖ → HШ → ЖZ → ΥΚ → 9а → ЦJ → Вd → ΜΣ → 5д → ЮB → ТN → τl → vκ → bД → ΠΞ
31 cycle 2 nodesΞйΠ → ΟйΟ
4154 cycles24 nodesD0иЭ → иПP2 → жοp4 → вmς8 → ЪsμG → КgψW → δΕΩΓ → PIЦС → Дρnc → ΠqξΟ → l0иυ → иwθ2 → жYЖ4 → вΦΘ8 → ЪCЬG → РЙVQ → πγΒq → nOРσ → ςsμo → rgψο → Ζkτα → xIЦι → ДYЖc → ΧΟΞΙ
51 cycle (fixed) 1 node ρoйπp