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 steps1 → 0 → 0
215 max steps10 → 0γ → β1 → Ω3 → Υ7 → ΜF → vV → PΒ → bp → DΞ → zR → Xt → LΖ → jh → 1β → Ω3
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 → iγi → hγj → iγi
415 max stepsj000 → iγγi → ihij → 1γγβ → β0β2 → βΨ32 → ΩΤ74 → ΥΛF8 → ΜuVG → vOΒW → dOΒo → dAΠo → ΖAΠM → ΖihM → j0βi → β0β2
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 → yUγvT → xTγwU → xSγxU → ySγxT → yUγvT
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 → ΔbPΑpO → fbDΝpm → zE6ΥΝS → ΞyWtSE → zWMΔuS → hXNΓtk → fM2ΩΕm → Χi6Υi6 → ΠΝγγDC → ΟΞ2ΩDD → ΧΒzQP6 → ΠcYroC → ΔJBΟΘO → ΔoelcO → fC6ΥΟm → ΞΓ6ΥOE → ΞzdmRE → zY8ΣsS → ΚXJΗtI → rnLΕda → jH9ΡΚi → Θs0βYK → βnJΗd2 → Ωn9Ρd4 → ΥΘ9ΡJ8 → ΜΘncJG → voAΠcW → ΖPBΟΒM → ΔjbohO → fD1αΞm → ΩΑ6ΥQ4 → ΥΞZqD8 → ΜΑGΚQG → vtZqXW → PMGΚΕΓ → ticniY → LAγγΠΗ → ΡΖ8ΣLB → ΚΖjgLI → rk2Ωga → ΧH3ΨΚ6 → ΥΠrYB8 → ΜΕIΘMG → vphibW → PE0βΝΓ → βycnS2 → ΩWAΠu4 → ΥΖNΓL8 → ΜkelgG → v73ΨΥW → ΥΝOΒE8 → ΜycnSG → vWAΠuW → ΖPNΓΒM → jfboli → D60βΦΟ → βΟΑPC2 → ΩΓapO4 → ΥeEΜm8 → Μx7ΤTG → ΜvTwVG → vTPΑxW → bUOΒwq → dSEΜyo → xWAΠuU → ΖTNΓxM → jfTwli → T60βΦy → βΟUvC2 → ΩΓQzO4 → ΥeYrm8 → ΜJ7ΤΘG → ΜvncVG → vQAΠΑW → ΖaOΒqM → jdFΛni → vA0βΡW → βΗOΒK2 → Ωmcne4 → ΥB7ΤΠ8 → ΝΛΔMGF → xugjWU → TO2ΩΓy → ΧeUvm6 → ΠR7ΤzC → ΜΔXsNG → vgKΖkW → lP3ΨΒg → Υc4Χo8 → ΣΜBΟFA → ΘΔvUNK → ngQzke → Z93ΨΣs → ΥΙIΘI8 → ΜqobaG → vGCΞΛW → ΒuOΒWQ → dbNΓpo → fEAΠΝm → Ζy6ΥSM → ΞjVuhE → zP1αΒS → ΩcWto4 → ΥNBΟΔ8 → ΜΔfkNG → vg4ΧkW → ΣP3ΨΒA → ΥΘboJ8 → ΜoCΞcG → ΒvBΟVQ → ΔbPΑpO
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 → ΕjLγΕhN → ΖhMγΔjM → ΕjLγΕhN