Base 67: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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 cycles4 nodesBt → hN → Jl → Rd
31 cycle 2 nodesWΕY → XΕX
416 cycles33 nodesB2Βu → ziL6 → tMhC → hKjO → PIlg → TGnc → X8vY → n0ΔI → ΔUZ2 → Β4z4 → xu98 → pkJG → ZQdW → D2Βs → zeP6 → tEpC → haTO → J6xm → rSbE → d8vS → nAtI → jUZM → N4zi → vKjA → lOfK → RGne → XCrY → f0ΔQ → ΔEp2 → ΒaT4 → x6x8 → roFE → dYVS
52 cycles4 nodesiLΕiN → jKΕjM → kMΕhL → jNΕgM
65 cycles14 nodesTJ9ulc → lS8vcK → nR9udI → lVBsZK → hR3ΑdO → xJBsl8 → phRcNG → ZKAtkW → jQ2ΒeM → zNDqh6 → tdJkRC → hRBsdO → hJBslO → hSIlcO
71 cycle 8 nodesoXDΕqXH → rZGΕnVE → qbHΕmTF → pZIΕlVG → oXFΕoXH → pXGΕnXG → oZFΕoVH → pXIΕlXG
87 cycles40 nodesRDA1Γure → ΒkeCrQK4 → xfQDqeP8 → pdGDqoRG → dZYBsWVS → hB41ΓΑtO → ΒwiIlM84 → xoTLibG8 → pYN7whWG → pZK1ΓkVG → ΒZQ3ΑeV4 → ywE3Αq87 → xrobSGD8 → peY8vWQG → nZE1ΓqVI → ΒcV3ΑZS4 → ywA3Αu87 → xrojKGD8 → peYOfWQG → ZHE1ΓqnW → ΒcW2ΒYS4 → zxA1Γu76 → ΒtqjKEB4 → xicOfSM8 → pMH9uniG → lZWLiYVK → RN41ΓΑhe → ΒwKCrk84 → xofPePG8 → pYGEpoWG → bZY1ΓWVU → Β741ΓΑx4 → ΒxwpE874 → xqoaTGE8 → pcY6xWSG → rZA1ΓuVE → Βkd3ΑRK4 → ywQBse87 → rohDqNGE → ecYJkWSR