Base 89: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0γ → β1 → Ω3
345 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
44 max stepsj000 → iγγi → ihij → 1γγβ → β0β2
535 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
6176 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
746 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