Base 89: 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--
25 cycles12 nodes1β → Ω3 → Υ7 → ΜF → vV → PΒ → bp → DΞ → zR → Xt → LΖ → jh
31 cycle 2 nodeshγj → iγi
486 cycles11 nodesN0βΕ → βgj2 → Ω2Ω4 → ΧΤ76 → ΠΛFC → ΔuVO → fOΒm → d6Υo → ΞAΠE → ΖyRM → jWti
51 cycle 4 nodesxSγxU → ySγxT → yUγvT → xTγwU
69 cycles158 nodesD91αΣΟ → ΩΙΑPI4 → Υqapa8 → ΜGEΜΛG → xvtWVU → TQMΔΑy → haUvqk → RG2ΩΛΑ → ΧuYrW6 → ΠOIΘΓC → ΔpdmbO → fE8ΣΝm → Κy6ΥSI → ΞrVuZE → zPHΙΒS → rcWtoa → NHBΟΚΕ → ΔsgjYO → fK2ΩΗm → Χm6Υe6 → ΠΞ7ΤDC → ΜΔzQNG → vgYrkW → PJ3ΨΘΓ → Υocnc8 → ΜCAΠΟG → ΖΓuVOM → jeOΒmi → d80βΤo → βΛAΠG2 → ΩΖtWL4 → ΥkMΔg8 → Μh3ΨjG → Υv1αV8 → ΩΜPΑF4 → ΥwapU8 → ΜSEΜyG → xvVuVU → TQOΒΑy → daUvqo → RGAΠΛΑ → ΖuYrWM → jOIΘΓi → pe0βmc → βD7ΤΞ2 → ΩΜzQF4 → ΥwYrU8 → ΜSIΘyG → vpVubW → QODΝΓΒ → zeapmS → XF7ΤΜu → ΜwMΔUG → vhRyjW → XP1αΒu → ΩcMΔo4 → ΥhBΟj8 → ΜΔ1αNG → ΩvfkV4 → ΥQ4ΧΑ8 → ΣΜZqFA → ΘwGΚUK → tnRydY → XL9ΡΖu → ΘkMΔgK → nh3Ψje → Υ91αΣ8 → ΩΜΘIF4 → ΥwobU8 → ΜSCΞyG → ΒvVuVQ → bQOΒΑq → daEΜqo → xGAΠΛU → ΖuSxWM → jVNΓvi → fQ0βΑm → βa6Υq2 → ΩΞFΛD4 → ΥΑuVQ8 → ΜaOΒqG → vdFΛnW → vP9ΡΒW → ΘcOΒoK → ndBΟne → ΔA8ΣΡO → ΚΗelKI → rm6Υea → ΞH7ΤΚE → ΜzrYRG → vYIΘsW → pPJΗΒc → ncCΞoe → ΒC8ΣΟQ → ΚΓapOI → reEΜma → xH7ΤΚU → ΜsSxYG → vVJΗvW → nQOΒΑe → da8Σqo → ΚGAΠΛI → ΖuqZWM → jOGΚΓi → te0βmY → βL7ΤΖ2 → ΩΜjgF4 → Υw2ΩU8 → ΧΜRyF6 → ΠwWtUC → ΔSMΔyO → hfVulk → P62ΩΦΓ → ΧΟcnC6 → ΠΓAΠOC → ΖΔdmNM → jg8Σki → Κ40βΨI → βΤqZ82 → ΩΛGΚG4 → ΥusXW8 → ΜOKΖΓG → vldmfW → P95ΦΣΓ → ΠΙcnIC → ΔqAΠaO → ΖfFΛlM → vj5ΦhW → ΠP1αΒC → ΩΔboN4 → ΥgCΞk8 → ΜΒ3ΨPG → ΥvboV8 → ΜQCΞΑG → ΒvZqVQ → bQGΚΑq → taEΜqY → xLFΛΖU → vkSxgW → VP3ΨΒw → ΥcQzo8 → ΜZBΟrG → ΔvHΙVO → rfPΑla → bH5ΦΚq → ΠsEΜYC → ΔxJΗTO → nfTwle → T95ΦΣy → ΠΙUvIC → ΔqQzaO → fZFΛrm → vI6ΥΙW → ΞqOΒaE → zdFΛnS → vX9ΡtW → ΘPLΕΒK → njbohe
73 cycles4 nodesΔhKγΖjO → ΗhLγΕjL → ΖlMγΔfM → ΕjNγΓhN