Base 96: 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
226 max steps20 → 1ι → η3γ7ΤFΓVYzgrΝLqhΡHyZknε5ΨBΛNmlι1η3
350 max steps100 → 0κκ → ικ1 → θκ2 → ηκ3 → ζκ4 → εκ5 → δκ6 → γκ7 → βκ8 → ακ9 → ΩκA → ΨκB → ΧκC → ΦκD → ΥκE → ΤκF → ΣκG → ΡκH → ΠκI → ΟκJ → ΞκK → ΝκL → ΜκM → ΛκN → ΚκO → ΙκP → ΘκQ → ΗκR → ΖκS → ΕκT → ΔκU → ΓκV → ΒκW → ΑκX → zκY → yκZ → xκa → wκb → vκc → uκd → tκe → sκf → rκg → qκh → pκi → oκj → nκk → mκl → lκmlκm
431 max steps3006 → 62ηε → εΧB6 → ΨΚNC → ΛllO → lκκm → mkmm → 1κκι → ι0ι2 → ιζ32 → ηβ74 → γΣF8 → ΤΒVG → ΓVΒWXUΓΒYTΔΑaRΖyeNΚumFΣmΒκκWΒVΒXWTΔΓaVΒyWNΚΓmVΒmVκκΓΓUΓWYVΒΑWRΖΓeVΒuWFΣΓΓVΒW
541 max steps10009 → 90κιβ → κΨκA1 → ιΨκA2 → θΧκB3 → ηΥκD4 → ζΡκG5 → εΝκK6 → δΘκP7 → γΒκV8 → βuκc9 → αmκkA → ΩdκtB → ΨjκnC → ΧcκuD → ΦiκoE → ΥbκvF → ΤhκpG → ΣaκwH → ΡgκqI → ΠZκxJ → ΟfκrK → ΞYκyL → ΝeκsM → ΜXκzN → ΛdκtO → ΚWκΑP → ΙcκuQ → ΘVκΒR → ΗbκvS → ΖUκΓT → ΕaκwU → ΔTκΔV → ΕXκzU → ΔWκΑV → ΓWκΑW → ΒVκΒX → ΓTκΔW → ΕWκΑU → ΔXκzV → ΓVκΒWΓVκΒW
6389 max stepsX000ΒΒ → ΒΒWΑWX → VVSΕΓΔ → cYWΑzw → URJΞΗΕ → ufZxse → OGCΦΣΛ → ΙΒllWQ → iUκκΓq → ΔpBΧiV → ΛY6γzO → ΦmQΗlE → Ηg0ιrS → ιeAΨt2 → ηΝEΤL4 → γΕqgT8 → Τb9ΩwG → ΟΓKΝVK → usWΑfe → UGCΦΣΕ → ΙΒZxWQ → iVNΚΓq → mX7βΑm → ΤSκκΕG → ΣΖDΥSH → ΗΑcuXS → eTHΠΕu → ybFΣwa → ΓOKΝΚW → slVΒmg → WC0ιΧΓ → ιΚVΒO2 → ηlVΒm4 → γW0ιΒ8 → ιΤUΓF2 → ηΔXzU4 → γZRΖy8 → ΤeOΙtG → ΓkEΤnW → ΕW2ηΒU → εaUΓx6 → ΨYMΛzC → ΛoQΗjO → mg4εrm → αAκκΨA → ΩΩ1θAB → ηΞΜLK4 → γtphe8 → ΤF7βΤG → ΤΔΒVUG → ΓZVΒyW → XVOΙΓΒ → kXTΔΑo → aT3ζΕy → γbNΚw8 → ΤmKΝlG → Γs0ιfW → ιWCΦΒ2 → ηΙUΓP4 → γjXzo8 → ΤS4εΖG → αΓcuVA → ΟXHΠΑK → yuSΕda → cOGΡΚw → ΑlJΞmY → uS0ιΖe → ιdFΣu2 → ηΓGΡV4 → γΑWΑX8 → ΤUSΕΔG → ΓcYyvW → WQIΟΘΓ → whVΒqc → WK8αΞΓ → ΡtVΒeI → yWEΤΒa → ΕVNΚΓU → maWΑxm → UMκκΛΕ → ΜΔ5δUN → ΨoYyjC → ΛQ4εΘO → αmgqlA → ΟA0ιΩK → ιΞtdK2 → ηtFΣe4 → γΓEΤV8 → ΤΕWΑTG → ΓbTΔwW → aWKΝΒy → sVNΚΓg → mXBΧΑm → ΛSκκΕO → ΚΖ5δSP → ΨkcunC → ΛI2ηΠO → εxlla6 → ΨMκκΛC → ΧΜBΧMD → ΛΙoiPO → mj5δom → Ψ4κκεC → ζΧ5δC5 → αΨΙOBA → ΟΜjnMK → up3ζie → γG6γΣ8 → ΦΤΑWFE → ΗΔTΔUS → eaYyxu → QNFΣΛΙ → ΓnhpkW → W82ηβΓ → εΣVΒG6 → ΨΒVΒWC → ΛWUΓΒO → mYUΓzm → YQκκΗΑ → Θz5δYR → ΨgQΗrC → ΛgAΨrO → ΝmAΨlM → Νq0ιhM → ιq8αh2 → ηΡ8αH4 → γΡyYH8 → ΤzPΘYG → ΓiQΗpW → gW6γΒs → ΦVBΧΓE → ΛΗWΑRO → mfTΔsm → aCκκΦy → ΧxLΜaD → ΙqMΛhQ → oi8αpk → Ρ73ζγI → γΥxZE8 → ΤΖNΚSG → ΓmculW → WI0ιΠΓ → ιxVΒa2 → ηWMΛΒ4 → γoUΓj8 → ΤY4εzG → αΓQΗVA → ΟgWΑrK → uUAΨΔe → ΝZFΣyM → ΓqOΙhW → kW8αΒo → ΡV3ζΓI → γyWΑZ8 → ΤUOΙΔG → ΓkYynW → WQ2ηΘΓ → εhVΒq6 → ΨW8αΒC → ΡΛUΓNI → ynXzka → SO2ηΚΗ → εldtm6 → ΨG0ιΣC → ιΛΑWN2 → ηnTΔk4 → γa2ηx8 → εΤMΛF6 → ΨΔnjUC → ΛZ3ζyO → γmOΙl8 → Τk0ιnG → ιΓ2ηV2 → ηεWΑ54 → γΩTΔA8 → ΤΞZxKG → ΓtNΚeW → mWEΤΒm → ΕUκκΓU → ΔΔ1θUV → ηZXzy4 → γSOΙΖ8 → ΤkcunG → ΓI2ηΠW → εxVΒa6 → ΨWMΛΒC → ΛoUΓjO → mY4εzm → αQκκΗA → ΩΘHΠQB → ΝygqZM → qP9ΩΙi → Οj7βoK → Τu4εdG → αΓGΡVA → ΟΑWΑXK → uUSΕΔe → cZFΣyw → ΓPJΞΙW → ujVΒoe → WG4εΣΓ → αΒVΒWA → ΟWUΓΒK → uYUΓze → YRFΣΗΑ → ΓfRΖsW → eWCΦΒu → ΙVFΣΓQ → ΓiWΑpW → WU6γΔΓ → ΦZVΒyE → ΗWOΙΒS → keUΓto → YF3ζΤΑ → γΔRΖU8 → ΤeYytG → ΓQEΤΘW → ΕhVΒqU → aW8αΒy → ΡVNΚΓI → ymWΑla → UO0ιΚΕ → ιlZxm2 → ηO0ιΚ4 → ιγkm72 → ηΥ1θE4 → ηγΕS74 → γΥbvE8 → ΤΖJΞSG → ΓucudW → WIGΡΠΓ → ΑxVΒaY → WSMΛΖΓ → odVΒuk → WH3ζΡΓ → γzVΒY8 → ΤWQΗΒG → ΓgUΓrW → YWAΨΒΑ → ΝVRΖΓM → qeWΑti → UF7βΤΕ → ΤΔZxUG → ΓZNΚyW → mWOΙΒm → kUκκΓo → ΔnDΥkV → ΗY2ηzS → εeQΗt6 → ΨgEΤrC → ΛΕAΨTO → ΝmawlM → qM0ιΜi → ιp7βi2 → ηΤ6γF4 → γΦΓUD8 → ΤΘXzQG → ΓhRΖqW → eW8αΒu → ΡVFΣΓI → ΓyWΑZW → WUOΙΔΓ → kZVΒyo → WP3ζΙΓγjVΒo8ΤW4εΒGαΓUΓVAΟYWΑzKuUQΗΔegZFΣysΓPBΧΙWΛjVΒoOmW4εΒmαUκκΓAΩΔLΜUBΝqYyhMqQ8αΘiΡh7βqIΤy8αZGΡΓOΙVIykWΑnaUO2ηΚΕεlZxm6ΨO0ιΚCιΛkmN2ηn1θk4ηγ2η74εγΤE76ΨΥΔTECΛΖZxSOmdNΚummGκκΡmΣlTΔmHΑa0ιxYιSMΛΖ2ηocuj4γI4εΠ8αΤwaFAΟΔLΜUKuqYyheQG8αΣΙΡΒhpWIyV7βΓaΤXNΚΑGΓmSΕlWcW0ιΒwιVJΞΓ2ηuWΑd4γUGΡΔ8ΤΑYyXGΓTPΘΕWibVΒwqWL7βΝΓΤrVΒgGΓWAΨΒWΝWUΓΒMqYUΓziYR7βΗΑΤfRΖsGΓeCΦtWΙWEΤΒQΕiUΓpUaY6γzyΦRNΚΗEΗmeslSeE0ιΥuιΖFΣS2ηΓcuV4γXHΠΑ8ΤySΕZGΓcOΙvWkWIΟΒowV3ζΓcγXJΞΑ8ΤuSΕdGΓcGΡvWΑWIΟΒYwVRΖΓceXJΞΑuuTFΣΕeΓbFΣwWΓWKΝΒWsWUΓΒgYVBΧΓΑΛXRΖΑOmeSΕtmcEκκΤwΥvLΜcFΕqIΟhUwa8αxcΡNJΞΛIyumkdaOH1θΡΛηzllY4γQκκΗ8βΘJΞQ9ΡugqdIyH9ΩΡaΟzNΚYKumQΗlegG0ιΣsιΒBΧW2ηΛUΓN4γnXzk8ΤS2ηΖGεΓcuV6ΨXHΠΑCΛySΕZOmcOΙvmkIκκΟoΠnPΘkJwi2ηpcεK6γΞ6ΨΦseDCΛΘDΥQOΗmgqlSeA0ιΩuιΞFΣK2ηΓseV4γXDΥΑ8ΤΗSΕRGΓfbvsWWKCΦΞΓΙtVΒeQiWEΤΒqΕV7βΓUΤaWΑxGΓUMΛΔWoZVΒykWP3ζΙΓ
753 max steps1000000 → 0κκκκκκ → ικκκκκ1 → ι0κκκι2 → κθ0κι21 → κιζκ311 → ιιεκ412 → ιηδκ532 → θζακ843 → ηδΦκC64 → ζαΟκI95 → εΦΖκRD6 → δΠsκeI7 → γΚaκwO8 → βΓYκyV9 → αuTκΔdA → ΩvPκΘcB → ΨyUκΓZC → ΧsSκΕfD → ΦtOκΙeE → ΥwTκΔbF → ΤqRκΖhG → ΣrNκΚgH → ΡuSκΕdI → ΠoQκΗjJ → ΟpMκΛiK → ΞsRκΖfL → ΝmPκΘlM → ΜnLκΜkN → ΝoQκΗjM → ΜmMκΛlN → ΜoOκΙjN → ΛnOκΙkO → ΚmNκΚlP → ΛkNκΚnOΛmOκΙlOΚmMκΛlPΜlNκΚmNΛoNκΚjOΛmPκΘlOΚlLκΜmPΝmNκΚlMΜpNκΚiNΛoQκΗjOΚkMκΛnPΜlOκΙmNΛnMκΛkOΜmPκΘlNΛmLκΜlOΝnOκΙkMΜoNκΚjNΛoPκΘjOΚlNκΚmPΛkNκΚnO