Base 103: 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--
21 cycle 6 nodes7κ → βF → ΚV → dΒ → NΣ → tl
31 cycle 2 nodesoρq → pρp
425 cycles51 nodesF6κγ → δΛTE → ΞgxS → lGΩu → Θ8θY → ΩYΖI → ΖWΘa → bUΚΕ → fSΜΑ → jKΥw → zCδg → ΠIΧQ → Δopc → R0πΟ → πmr2 → ξ4μ4 → κη98 → βΦJG → ΚΑdW → dMΣΓ → vOΠk → rAζo → Υ2ξM → μwh6 → ζEβC → ΣΛTO → tgxm → H6κα → δΗXE → ΞYΖS → lWΘu → b8θΕ → ΩSΜI → Ζiva → VCδΛ → ΠezQ → pKΥq → z0πg → πIΧ2 → ξΓb4 → κQΞ8 → βmrG → Κ4μW → θcΒA → ΧOΠK → Βqne → N2ξΤ → μuj6 → ζAζC → ΥΡNM → xsli
52 cycles4 nodesΗXρΗZ → ΘWρΘY → ΙYρΖX → ΘZρΕY
66 cycles28 nodesRK6κΦΟ → δΑmreE → ΞM4μΤS → θwktiA → ΧE8θγK → ΩΝΑdSI → ΖkMΣua → vV9ηΚk → ΧeAζΑK → ΥΒLΤdM → ywNΡih → tHDγΩm → ΞΗ6κYS → δlXΗtE → ΞZ7ιΖS → βlVΙtG → Κd7ιΒW → βdNΡΒG → ΚtNΡlW → td7ιΒm → βO6κΡG → δΚrmVE → Ξe4μΑS → θlLΤtA → Χx7ιhK → βΒFαdG → ΛΙNΡWV → tfbΓzm