Base 85: Maximum Iteration Sequences: Full Cycle

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 Max Steps Max Step Example
Full Cycle
12 max steps100
210 max steps10 → 0Ψ → Χ1 → Υ3Π7ΘFrVfhΥ3
345 max steps100 → 0ΨΨ → ΧΨ1 → ΦΨ2 → ΥΨ3 → ΤΨ4 → ΣΨ5 → ΡΨ6 → ΠΨ7 → ΟΨ8 → ΞΨ9 → ΝΨA → ΜΨB → ΛΨC → ΚΨD → ΙΨE → ΘΨF → ΗΨG → ΖΨH → ΕΨI → ΔΨJ → ΓΨK → ΒΨL → ΑΨM → zΨN → yΨO → xΨP → wΨQ → vΨR → uΨS → tΨT → sΨU → rΨV → qΨW → pΨX → oΨY → nΨZ → mΨa → lΨb → kΨc → jΨd → iΨe → hΨf → gΨgfΨhgΨg
412 max stepsh000 → gΨΨg → gfgh → 1ΨΨΧ → Χ0Χ2ΧΤ32ΥΟ74ΠΗF8ΘqVGrKΒWhKΒgh0ΧgΧ0Χ2
537 max steps1000C → C0ΨΧΜ → ΨΙΨD1 → ΧΙΨD2 → ΦΘΨE3 → ΥΖΨG4 → ΤΓΨJ5 → ΣyΨN6 → ΡtΨS7 → ΠnΨY8 → ΟgΨf9 → ΞYΨnA → ΝeΨhB → ΜXΨoC → ΛdΨiD → ΚWΨpE → ΙcΨjF → ΘVΨqG → ΗbΨkH → ΖUΨrI → ΕaΨlJ → ΔTΨsK → ΓZΨmL → ΒSΨtM → ΑYΨnN → zRΨuO → yXΨoP → xQΨvQ → wWΨpR → vPΨwS → xTΨsQ → wTΨsR → vSΨtS → uSΨtT → uQΨvTwRΨuRvUΨrSuQΨvT
6172 max stepsZ000ΒΒ → ΒΒYnLM → gfEΘhh → t20ΧΦU → ΧΤOx42 → ΥΟYn84 → ΠΗEΘG8 → ΘtpWTG → rQIΔwW → lWKΒqc → hK8ΞΓg → Ζi0ΧeI → Χn3ΤZ2 → ΥΠDΙ74 → ΠΙuRE8 → ΘuStSG → rSQvuW → VSKΒus → hSMzug → dS0Χuk → ΧS6Πu2 → ΥΚRuD4 → ΠwStQ8 → ΘWQvqG → rVJΓrW → jMKΒΑe → he4Σig → Ξ40ΧΤA → ΧΟΓJ82 → ΥΗidG4 → Πq4ΣW8 → ΞΘJΓFA → ΔsidUK → jO4Σye → Ξa4ΣmA → ΞΔBΛJA → ΔzjcNK → jc6Πke → Κ84ΣΟE → ΞΗuRGA → ΔqStWK → jRJΓve → jU4Σse → ΞO4ΣyA → ΞΔZmJA → ΔkCΚcK → xj7ΟdQ → ΘX5ΡpG → ΜrHΕVC → znLΑZO → fbDΙli → vA2ΥΝS → ΣΓStK6 → ΜiQveC → zV3ΤrO → ΠbLΑl8 → Θf9ΝhG → Δr1ΦVK → ΥjLΑd4 → Πf5Ρh8 → ΜΘ1ΦFC → ΥzrUN4 → ΠcMzk8 → Θd7ΟjG → Θr5ΡVG → ΜrLΑVC → zfLΑhO → fb1Φli → ΥA2ΥΝ4 → ΣΠΒK76 → ΜΙgfEC → zu0ΧSO → ΧbRul2 → ΥT9Νt4 → ΠΔPwJ8 → ΘkWpcG → rJ7ΟΔW → ΘkKΒcG → rh7ΟfW → ΘL1ΦΒG → ΥrfgV4 → ΠM0ΧΑ8 → ΧΘdiF2 → Υs4ΣU4 → ΠΞNy98 → ΘΕalIG → rmAΜaW → ΒLBΛΒM → zgehgO → b2ΨΨΥm → ΦlWpb3 → ΣJ9ΝΔ6 → ΜΔjcJC → zk6ΠcO → Κb7ΟlE → Θv9ΝRG → ΔrTsVK → jPLΑxe → fY4Σoi → ΞG2ΥΗA → ΣΔpWJ6 → ΜkIΔcC → zl7ΟbO → Θb9ΝlG → Δr9ΝVK → ΔjLΑdK → jf5Ρhe → Μ51ΦΣC → ΥΝyNA4 → ΠΓalK8 → ΘiAΜeG → Βr3ΤVM → ΠfLΑh8 → Θf1ΦhG → Υr1ΦV4 → ΥΠLΑ74 → ΠΙehE8 → Θu2ΥSG → ΣrRuV6 → ΜTLΑtC → zfPwhO → bX1Φpm → ΥIAΜΕ4 → ΠΒlaL8ΘgAΜgGΒqΨΨVMΑrAΜVNΒdLΑjMge5ΡihΜ40ΧΤCΧΟyN82ΥΗalG4ΠqAΜW8ΘΒJΓLGrjfgdWL60ΧΡΓΧΛgfC2Υy0ΧO4ΧΠZm72ΥΙCΚE4ΠxtSP8ΘYQvoGrVFΗrWrMKΒΑWheKΒigh40ΧΤgΧΟ0Χ82ΧΥΖG32ΥΡoX64ΠΛGΖC8ΘyoXOGraGΖmWpLBΛΒYzgGΖgOpaΨΨlYom3ΤaZΠFBΛΘ8ΘzrUNGrcMzkWdL7ΟΒkΘg6ΠgGΚqΨΨVEΙrIΔVFtlLΑbUfP9ΝxiΔY2ΥoKΣjFΗd6Μr5ΡVCΜzLΑNCzfbkhOb91ΦΞmΥΕAΜI4ΠΒlaL8
745 max steps1000016 → 610ΨΧΧΣ → ΨΦΟΨ721 → ΧΦΝΨ922 → ΦΥΛΨB33 → ΥΣΘΨE54 → ΤΟΓΨJ85 → ΣΛuΨRC6 → ΡΖiΨdH7 → ΠzRΨuN8 → ΟsXΨoU9 → ΞkKΨΒcA → ΝtOΨxTB → ΜoTΨsYC → ΛiJΨΓeD → ΚrNΨyVE → ΙmSΨtaF → ΘgIΨΔgG → ΗpMΨzXH → ΖkRΨucI → ΕeHΨΕiJ → ΖlPΨwbI → ΕgKΨΒgJ → ΔkKΨΒcK → ΓjOΨxdL → ΒeJΨΓiM → ΔgMΨzgK → ΓhIΨΔfL → ΕiMΨzeJ → ΔiKΨΒeK → ΓjMΨzdL → ΒgLΨΑgM → ΒfJΨΓhM → ΔgLΨΑgK → ΓiJΨΓeL → ΔhNΨyfK → ΓgIΨΔgL → ΕiLΨΑeJ → ΔjLΨΑdK → ΓiMΨzeL → ΒgKΨΒgM → ΓfKΨΒhL → ΓhLΨΑfL → ΒhKΨΒfMΓfLΨΑhLΒhKΨΒfM