Base 89: 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
215 max steps10 → 0γ → β1 → Ω3Υ7ΜFvVbpzRXtjhΩ3
347 max steps100 → 0γγ → βγ1 → αγ2 → Ωγ3 → Ψγ4 → Χγ5 → Φγ6 → Υγ7 → Τγ8 → Σγ9 → ΡγA → ΠγB → ΟγC → ΞγD → ΝγE → ΜγF → ΛγG → ΚγH → ΙγI → ΘγJ → ΗγK → ΖγL → ΕγM → ΔγN → ΓγO → ΒγP → ΑγQ → zγR → yγS → xγT → wγU → vγV → uγW → tγX → sγY → rγZ → qγa → pγb → oγc → nγd → mγe → lγf → kγg → jγh → iγihγjiγi
415 max stepsj000 → iγγi → ihij → 1γγβ → β0β2βΨ32ΩΤ74ΥΛF8ΜuVGvOΒWdOΒodAΠoΖAΠMΖihMj0βiβ0β2
539 max stepsh0000 → gγγγk → kfγkh → l2γΩg → αgγj3 → Ωhγi4 → Ψfγk5 → Χgγj6 → Φeγl7 → Υfγk8 → Τdγm9 → ΣeγlA → ΡcγnB → ΠdγmC → ΟbγoD → ΞcγnE → ΝaγpF → ΜbγoG → ΛZγqH → ΚaγpI → ΙYγrJ → ΘZγqK → ΗXγsL → ΖYγrM → ΕWγtN → ΔXγsO → ΓVγuP → ΒWγtQ → ΑUγvR → zVγuS → yTγwT → xUγvU → wSγxV → yRγyT → zUγvS → yUγvTxTγwUxSγxUySγxTyUγvT
6286 max stepsH000JP → PJGΚΘΓ → tocncY → LCAΠΟΗ → ΖΓkfOM → je4Χmi → Σ80βΤA → βΛΗJG2 → ΩumdW4 → ΥO8ΣΓ8 → ΜΚdmHG → vs8ΣYW → ΚPJΗΒI → rnboda → HD9ΡΞΛ → ΘΑsXQK → naKΖqe → lG8ΣΛg → Κu4ΧWI → ΣrNΓZA → ΘfHΙlK → rn5Φda → ΠH9ΡΚC → ΘΔrYNK → ngIΘke → p93ΨΣc → ΥΙCΞI8 → ΜΒpaPG → vcEΜoW → xPBΟΒU → ΔcSxoO → fVBΟvm → ΔQ6ΥΑO → ΞfZqlE → zH5ΦΚS → ΠsWtYC → ΔNJΗΔO → ngelke → 973ΨΥΤ → ΥΝΙHE8 → ΜyqZSG → vWGΚuW → tPNΓΒY → fcKΖom → lC6ΥΟg → ΞΓ4ΧOE → ΣzdmRA → ΘY8ΣsK → ΚnJΗdI → rn9Ρda → ΘH9ΡΚK → ΘsmdYK → nK8ΣΗe → Κm8ΣeI → Κr7ΤZI → ΜrHΙZG → vrHΙZW → rPHΙΒa → rcGΚoa → tHBΟΚY → ΔsKΖYO → lfJΗlg → n64ΧΦe → ΣΟ8ΣCA → ΚΘΒOJI → rocnca → HCAΠΟΛ → ΖΓsXOM → jeKΖmi → l80βΤg → βΛ4ΧG2 → ΩΣtW94 → ΥΙMΔI8 → ΜqgjaG → vG2ΩΛW → ΧuOΒW6 → ΠdNΓnC → Δf9ΡlO → Θf5ΦlK → Πn5ΦdC → ΠΔ9ΡNC → ΘΔfkNK → ng4Χke → Σ93ΨΣA → ΥΙΗJI8 → ΜqmdaG → vG8ΣΛW → ΚuOΒWI → rdNΓna → fH9ΡΚm → Θs6ΥYK → ΞnJΗdE → zn9ΡdS → ΘX9ΡtK → ΘnLΕdK → nj9Ρhe → Θ91αΣK → ΩΙmdI4 → Υq8Σa8 → ΜΚFΛHG → wurYWV → ROIΘΓΑ → peYrmc → JD7ΤΞΙ → ΜΑobQG → vaCΞqW → ΒPFΛΒQ → vcapoW → PFBΟΜΓ → ΔwcnUO → fSAΠym → ΖW6ΥuM → ΞjNΓhE → zf1αlS → ΩX5Φt4 → ΥΠLΕB8 → ΜΕihMG → vi0βiW → βOγγΒ2 → αΓNΓO3 → Χfdml6 → Π95ΦΣC → ΠΙΓNIC → ΔqelaO → fG6ΥΛm → Ξu6ΥWE → ΞzNΓRE → zfXslS → XL5ΦΖu → ΠkMΔgC → Δh3ΨjO → Υf1αl8 → ΩΜ5ΦF4 → ΥΠvUB8 → ΜΕQzMG → viYriW → PIγγΘΓ → ΙΒ4ΧPJ → ΣpbobA → ΘECΞΝK → ΒymdSQ → bW8Σuq → ΚOEΜΓI → xrdmZU → TI8ΣΙy → ΚqUvaI → rRFΛza → vYGΚsW → tPJΗΒY → ncKΖoe → lC8ΣΟg → ΚΓ4ΧOI → ΣrdmZA → ΘI8ΣΙK → ΚqmdaI → rG8ΣΛa → ΚuGΚWI → trNΓZY → fLHΙΖm → rk6Υga → ΞH3ΨΚE → ΥzrYR8 → ΜYIΘsG → vpJΗbW → nPDΝΒe → zc8ΣoS → ΚXBΟtI → ΔrLΕZO → jfHΙli → r60βΦa → βΟGΚC2 → ΩΓsXO4 → ΥeKΖm8 → Μl7ΤfG → Μv5ΦVG → ΠvPΑVC → ΔbPΑpOfbDΝpmzE6ΥΝSΞyWtSEzWMΔuShXNΓtkfM2ΩΕmΧi6Υi6ΠΝγγDCΟΞ2ΩDDΧΒzQP6ΠcYroCΔJBΟΘOΔoelcOfC6ΥΟmΞΓ6ΥOEΞzdmREzY8ΣsSΚXJΗtIrnLΕdajH9ΡΚiΘs0βYKβnJΗd2Ωn9Ρd4ΥΘ9ΡJ8ΜΘncJGvoAΠcWΖPBΟΒMΔjbohOfD1αΞmΩΑ6ΥQ4ΥΞZqD8ΜΑGΚQGvtZqXWPMGΚΕΓticniYLAγγΠΗΡΖ8ΣLBΚΖjgLIrk2ΩgaΧH3ΨΚ6ΥΠrYB8ΜΕIΘMGvphibWPE0βΝΓβycnS2ΩWAΠu4ΥΖNΓL8ΜkelgGv73ΨΥWΥΝOΒE8ΜycnSGvWAΠuWΖPNΓΒMjfboliD60βΦΟβΟΑPC2ΩΓapO4ΥeEΜm8Μx7ΤTGΜvTwVGvTPΑxWbUOΒwqdSEΜyoxWAΠuUΖTNΓxMjfTwliT60βΦyβΟUvC2ΩΓQzO4ΥeYrm8ΜJ7ΤΘGΜvncVGvQAΠΑWΖaOΒqMjdFΛnivA0βΡWβΗOΒK2Ωmcne4ΥB7ΤΠ8ΝΛΔMGFxugjWUTO2ΩΓyΧeUvm6ΠR7ΤzCΜΔXsNGvgKΖkWlP3ΨΒgΥc4Χo8ΣΜBΟFAΘΔvUNKngQzkeZ93ΨΣsΥΙIΘI8ΜqobaGvGCΞΛWΒuOΒWQdbNΓpofEAΠΝmΖy6ΥSMΞjVuhEzP1αΒSΩcWto4ΥNBΟΔ8ΜΔfkNGvg4ΧkWΣP3ΨΒAΥΘboJ8ΜoCΞcGΒvBΟVQΔbPΑpO
748 max stepsV00000i → iUγγγvj → wigγjiV → vG0γβΛW → γΚdγmH1 → βΚVγuH2 → αΙdγmI3 → ΩΗUγvK4 → ΨΔbγoN5 → ΧzRγyR6 → ΦuXγsW7 → ΥoMγΔc8 → ΤxQγzT9 → ΣsVγuYA → ΡmLγΕeB → ΠvPγΑVC → ΟqUγvaD → ΞkKγΖgE → ΝtOγΒXF → ΜoTγwcG → ΛiJγΗiH → ΚrNγΓZI → ΙmSγxeJ → ΘgIγΘkK → ΙnQγzdJ → ΘiLγΕiK → ΗmLγΕeL → ΖlPγΑfM → ΕgKγΖkN → ΗiNγΓiL → ΖjJγΗhM → ΘkNγΓgK → ΗkLγΕgL → ΖlNγΓfM → ΕiMγΔiN → ΕhKγΖjN → ΗiMγΔiL → ΖkKγΖgM → ΗjOγΒhL → ΖiJγΗiM → ΘkMγΔgK → ΗlMγΔfL → ΖkNγΓgM → ΕiLγΕiN → ΖhLγΕjM → ΖjMγΔhM → ΕjLγΕhNΖhMγΔjMΕjLγΕhN