Base 101: 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--
25 cycles8 nodes9ζ → ΥJ → zd → LΣ → vh → Dβ → ΜR → jt
31 cycle 2 nodesnοp → oοo
425 cycles50 nodesHAδΨ → ΣΕXM → vWΖi → ZCβΕ → ΞUΘQ → nczq → N2μΡ → κsj6 → δ8ζC → ΧΟNI → Δqla → T4κΛ → ζgvA → ΥEΩK → ΚydU → fKΣy → xIΥg → ΒGΧc → ΖOΞY → pWΖo → Z0ξΕ → ξUΘ2 → μcz4 → θMΠ8 → ΩsjG → Θ8ζW → ΧaΒI → ΔQΜa → lSΚs → h6θw → βEΩE → ΜΙTS → jexu → JAδΦ → ΣΑbM → vOΞi → pCβo → Ξ0ξQ → ξmp2 → μ2μ4 → κη76 → δΨFC → ΠΗVO → raΒm → R4κΝ → ζkrA → Υ6θK → βydE → ΜKΣS → xitg
51 cycle 4 nodesΖWοΖY → ΗWοΖX → ΗYοΔX → ΖXοΕY
613 cycles83 nodesF53λκα → θεΙTA8 → ΩΤexKG → ΘyIΥeW → ΒbJΤΒc → zQOΞΝe → pmKΣqo → x40ξλg → ξηGΧ82 → μΨΕXG4 → θΗWΖW8 → ΩaYΔΓG → ΘVRΛΘW → jcaΒΑu → ROAδΟΝ → ΣqkrmM → v73λθi → θαCβE8 → ΩΞΚSPG → ΘogvoW → bEοοΩΓ → αΒKΣbF → ΚxPΝfU → nfHΦxq → ΔI2μΦa → κΓSΚa6 → δhRΛvC → ΠjDαtO → Μr9εlS → Υj5ιtK → δz9εdC → ΥΠLΡNK → zvrkhe → LE6θαΤ → βΛwfSE → ΜiGΧuS → ΖjBγtY → ΠX9εΖO → ΥrXΕlK → zX5ιΖe → δYKΣΕC → ΠxVΗfO → rbHΦΒm → ΔQ4κΝa → ζmSΚqA → Υh3λvK → θzDαd8 → ΩΜLΡRG → ΘvjshW → bE8ζαΓ → ΧΛQΜSI → Δlhura → TD5ιβΛ → δΝgvQC → ΠmEΩqO → Κr3λlU → θf5ιx8 → δΩHΦFC → ΠΙΓZUO → reSΚym → hK4κΤw → ζyEΩeA → ΥΚJΤTK → Αyfwed → NKGΧΤΡ → ΖysjeY → XK8ζΤΗ → ΧyYΔeI → ΔVJΤΘa → zcSΚΑe → hOKΣΟw → xqEΩmg → ΚH3λΧU → θΕexY8 → ΩWIΥΗG → ΘΒZΓbW → bTPΝΚΓ → ngQΜwq → lG2μΨs → κΗ6θW6 → δβZΓDC → ΠΝSΚQO → rmgvqm