Base 97: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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--
22 cycles21 nodes1κ → θ3 → δ7 → ΥF → ΔV → XΒ → TΖ → bx → LΞ → rh → 9β → ΠJ → vd → HΣ → zZ → PΚ → jp → 5ζ → ΩB → ΜN → nl
31 cycle 2 nodeslλn → mλm
448 cycles24 nodesD8βΨ → ΣΙPI → zipa → P6δΛ → ΧknE → Θ2θS → ζet6 → ΩEΥC → ΜΕTO → naxm → N0κΝ → κoj2 → θ4ζ4 → δα98 → ΥΟJG → ΔudW → XGΣΓ → ΒUΔY → ZSΖΑ → dQΘw → hIΠs → xAΩc → ΞKΞM → tqhg
52 cycles4 nodesΓVλΓX → ΔUλΔW → ΕWλΒV → ΔXλΑW
67 cycles18 nodesPD1ιΧΛ → θΙknQ4 → δi2θq8 → ζΥ7γF6 → ΩΥΔUFC → ΜΕYzUO → naQΘym → hO0κΛs → κmAΩm2 → θΝλλL4 → ηΞIΠL5 → βxrgbA → ΠMAΩΝK → ΞvpidM → rI6δΡi → Χy8βaE → ΣΘNΛRI → znfsla
73 cycles4 nodesΚlMλΜnQ → ΝlNλΛnN → ΜpOλΚjO → ΛnPλΙlP