Base 147: 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--
21 cycle 18 nodes3а → Ь7 → ФF → ДV → ΧΒ → JР → φd → ΖΣ → BШ → МN → ξl → pκ → hς → xβ → RИ → ζt → ZА → ΞΚ
31 cycle 2 nodesΛгΝ → ΜгΜ
478 cycles42 nodesPAШЛ → ОλnM → ςkξi → xqθγ → fSЖυ → δΓΥw → VGТЕ → ВΨzY → ΣMМΗ → πAШk → ОsζM → ςaψi → ΜwβΝ → T0вЗ → вγv2 → аUД4 → ЬΨz8 → ФMМG → ДοjW → ΧsζΓ → bIРω → ψΛΜc → Κ0вΟ → в4Ю2 → аЩ94 → ЬПJ8 → ФυdG → ДΕΣW → ΧCЦΓ → КIРQ → ψιpc → ΚgςΟ → z4Юα → ЪOКA → РλnK → φkξe → ΖqθΤ → fCЦυ → КΓΥQ → κGТq → ВgςY → ΣyΩΗ
51 cycle (fixed) 1 node νmгμn