Base 83: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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 cycles6 nodes3Σ → Ξ7 → ΖF → pV → JΒ → hd
31 cycle 2 nodeseΦg → fΦf
420 cycles41 nodesD0ΥΙ → ΥuP2 → ΣUp4 → ΞKz8 → ΖefG → p0ΥW → ΥIΒ2 → Σib4 → Ξ6Ξ8 → ΘΕFE → toVS → RIΒu → jSrc → P6Ξw → ΘWnE → tGΔS → nQtY → TEΖs → rOvU → XMxo → bGΔk → n8ΜY → ΔEΖI → rkZU → NAΚy → zajM → d8Μi → Δ4ΠI → ΜkZA → ΒAΚK → zgdM → d2Σi → Π4Π6 → ΜΙBA → ΒwNK → hYle → D2ΣΙ → ΠuP6 → ΚUpC → xKzO → fYlg
51 cycle 4 nodestQΦtS → uQΦtR → uSΦrR → tRΦsS
66 cycles11 nodesig3Ρed → Ξ51ΤΠ8 → ΣΛΕFA4 → ΞΑoVK8 → ΖgIΒeG → pj1ΤbW → ΣJ7ΝΒ4 → ΞΖhcF8 → Ζq4ΠUG → ΜpLyVA → ΒdJΑhK
71 cycle 8 nodesΑfHΦΓfL → ΔhKΦzdI → ΓjLΦybJ → ΒhMΦxdK → ΑfJΦΑfL → ΒfKΦzfK → ΑhJΦΑdL → ΒfMΦxfK