Base 122: 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--
25 cycles20 nodes6Д → χD → ιR → Εt → AА → οL → Ρh → Yβ → qΘ → Gτ → γX → sΖ → Cψ → λP → Ιp → Iς → Ψb → kΞ → Sθ → Γv
31 cycle (fixed) 1 node yКz
415 cycles30 nodesE9Аχ → ρθRK → ΦΔte → g9АΤ → ρbΧK → ΦjΞe → gTζΤ → ΑbΧy → k1ИΟ → ЗTζ4 → Гzx8 → υ1ИG → ЗδV4 → ГvΒ8 → υ5ДG → ωδVC → νvΒO → Ν5Дm → ωPκC → νΘpO → ΝHςm → αPκa → ΙnΚq → MHςο → αΠha → oXβΛ → sLξΗ → ΡDφi → ιXβS → ΕrΖu
52 cycles4 nodesΥdКΥf → ΦdКΥe → ΦfКΣe → ΥeКΤf
69 cycles25 nodesQE6Гφλ → χθΘpSE → ιΔHςuS → αΕ8Бta → σoAωΚI → οαKοZM → ΤΡoΙhg → cZJπαΨ → ΦpjΞΙe → gUIρζΤ → ΨzbΧyc → lj0ЙΟΞ → ЙVRθε2 → ЗΕwΑt4 → ГB3Жω8 → ГυνMF8 → υζΞjUG → εzTζyW → Αw0ЙΒy → Й51ИЕ2 → ИЖωA43 → ЕВξL86 → ωτΠhGC → νδXβWO → ΝvrΖΓm