Base 109: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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
223 max steps10 → 0χ → φ1 → τ3π7θFΠVΜZvpμBΩNzlΥRrtτ3
357 max steps100 → 0χχ → φχ1 → υχ2 → τχ3 → σχ4 → ςχ5 → ρχ6 → πχ7 → οχ8 → ξχ9 → νχA → μχB → λχC → κχD → ιχE → θχF → ηχG → ζχH → εχI → δχJ → γχK → βχL → αχM → ΩχN → ΨχO → ΧχP → ΦχQ → ΥχR → ΤχS → ΣχT → ΡχU → ΠχV → ΟχW → ΞχX → ΝχY → ΜχZ → Λχa → Κχb → Ιχc → Θχd → Ηχe → Ζχf → Εχg → Δχh → Γχi → Βχj → Αχk → zχl → yχm → xχn → wχo → vχp → uχq → tχr → sχsrχtsχs
422 max stepst000 → sχχs → srst → 1χχφ → φ0φ2φσ32το74πηF8θΟVGΠiΒWjIδΓΚIδcΚWΞchWΞΕhMΩΕΒMΩkΒGζkΞGζYΞeΖYfQΥΗtQΥst0φsφ0φ2
545 max steps10006 → 60χφς → χοχ71 → φοχ72 → υξχ83 → τμχA4 → σιχD5 → ςεχH6 → ρΩχM7 → πΣχS8 → οΛχZ9 → ξΓχhA → νtχqB → μjχΑC → λpχuD → κiχΒE → ιoχvF → θhχΓG → ηnχwH → ζgχΔI → εmχxJ → δfχΕK → γlχyL → βeχΖM → αkχzN → ΩdχΗO → ΨjχΑP → ΧcχΘQ → ΦiχΒR → ΥbχΙS → ΤhχΓT → ΣaχΚU → ΡgχΔV → ΠZχΛW → ΟfχΕX → ΞYχΜY → ΝeχΖZ → ΜXχΝa → ΞbχΙY → ΝbχΙZ → ΜaχΚa → ΛaχΚb → ΛYχΜbΝZχΛZΜcχΘaΛYχΜb
6419 max stepsk000κκ → κκjΑDE → ΦΥGζRR → ΞtrsrY → f20φυΗ → φσQΥ42 → τοsr84 → πη0φG8 → φθΞWF2 → τΡgΔU4 → πmMΩy8 → θΒBλjG → ΩΠHεVO → ΜzjΑla → bHDιζΛ → ΥΝYΜYS → recΘΗu → VS2τΤΡ → ςqkzu6 → μF3σθC → πΩΠUN8 → θΑkzkG → ΠGEθηW → ΣΟiΒWU → niIδΓy → ΚKAμγc → βΗWΞeM → ΔhRΤΔi → rMKβαu → ΖΓ2τig → ςPJγΧ6 → μΘvodC → ΩU6πΡO → κzlylE → ΥECκιS → ΧΤqtSQ → vq2τuq → ς53σς6 → πνλBA8 → θγΨNKG → ΠΗyleW → jSCκΤΓ → ΧqIδuQ → Κv3σpc → πX5ρΞ8 → μθfΕFC → ΩΡOΧUO → zxlynm → EC9νλκ → δΨΤROK → Θyqtme → TC2τλΤ → ςΨovO6 → μy6πmC → κΩBλNE → ΩΥzkRO → zsEθsm → ΣCχχκU → λΡFηUD → ΧΠlyVQ → vkCκΑq → ΧG4ςηQ → ξΟupWA → δi4ςΓK → ξΘJγdA → δΘTΡdK → ΘnTΡxe → nT9νΣy → δoAμwK → βΘ7οdM → θΔTΡhG → ΠnLαxW → Δj9νΒi → δLHεβK → ΜΘΔgda → bUMΩΡΛ → ΒmYΜyk → dHBλζΙ → ΩΝUΠYO → zldΗzm → TECκιΤ → ΧΤovSQ → vq6πuq → κ53σςE → πνΤRA8 → θγqtKG → ΠΗ2τeW → ςjRΤΒ6 → μrHεtC → ΩΜ1υZO → τzbΙl4 → πXDιΞ8 → θΥfΕRG → ΠsOΧsW → xiχχΒo → Γw3σoj → πJ7οδ8 → ιηΘcGF → ΣΟUΠWU → nlhΓzy → LEAμιγ → βΤΕfSM → ΔqOΧui → xL3σβo → πΕ8ξg8 → θζNΨHG → ΠΝylYW → jeCκΗΓ → ΧSIδΤQ → Κvpupc → X64ςρΟ → ξλgΔCA → δΨMΩOK → ΘΒxmje → TIAμεΤ → βΛovaM → Δa6πΛi → κaKβΛE → ΥΖZΛfS → rbPΦΚu → vY2τΝq → ςe4ςΗ6 → ξμRΤBA → δαqtMK → ΘΓ2τie → ςTJγΣ6 → μΘnwdC → ΩU8ξΡO → ζzlylI → ΜECκιa → ΧΤaΚSQ → vqYΜuq → d53σςΙ → πνUΠA8 → θγkzKG → ΠΗEθeW → ΣjRΤΒU → rnHεxu → ΜA2τνa → ςγaΚK6 → μΗYΜeC → ΩdRΤΘO → zrTΡtm → nD1υκy → τΦAμQ4 → πβtqL8 → θΕ2τgG → ςΠNΨV6 → μzjΑlC → ΩHDιζO → ΥΝylYS → reCκΗu → ΧS2τΤQ → ςvpup6 → μ64ςρC → ξλΨNCA → δΨylOK → ΘyCκme → ΧTBλΣQ → ΩvnwpO → z95ρξm → μεCκIC → ΩΧΚaPO → zwYΜom → dD7οκΙ → θΦUΠQG → ΠukzqW → jF3σθΓ → πΡIδU8 → θΚlybG → ΠYCκΝW → ΧjdΗΒQ → vTHεΣq → Μo4ςwa → ξb7οΚA → θδXΝJG → ΠΙeΖcW → jWQΥΟΓ → tiIδΓs → ΚK0φγc → φΗWΞe2 → τhRΤΔ4 → πrLαt8 → θΔ1υhG → τΠLαV4 → πΔjΑh8 → θMGζαG → ΠΞΒiXW → jgIδΕΓ → ΚOIδΨc → ΚyWΞmc → hXBλΞΕ → ΩgMΩΕO → ΒzNΨlk → zHDιζm → ΥΝCκYS → ΧrdΗtQ → vT1υΣq → τo4ςw4 → πξ7ο98 → ιηδIGF → ΣΟΙbWU → niWΞΓy → hKAμγΕ → βΗMΩeM → ΔΒRΤji → rLHεβu → ΜΕ2τga → ςbNΨΚ6 → μzXΝlC → ΩfDιΖO → ΥzPΦlS → vrDιtq → Υ51υςS → τνqtA4 → πγ2τK8 → ςθΖeF6 → μΡQΥUC → ΩtlyrO → zD1υκm → τΦCκQ4 → πΧtqP8 → θw2τoG → ςΠ7οV6 → μθjΑFC → ΩΡGζUO → ΞzlylY → fECκιΗ → ΧΤQΥSQ → vtpurq → 641υσς → τολB84 → πηΨNG8 → θΟylWG → ΠiCκΓW → ΧjJγΒQ → ΘvHεpe → ΜT5ρΣa → μoaΚwC → ΩZ7οΜO → θzbΙlG → ΠXDιΞW → ΥjfΕΒS → rPHεΧuΜw2τoaςb7οΚ6μθXΝFCΩΡeΖUOzmQΥymtDBλκsΩΦ0φQOφztql2τE2τι4ςπΣS76μιovECΩΤ6πSOκzpulEΥE4ςιSξΤqtSAδq2τuKςΘ3σd6πμTΡB8θαmxMGΠΓAμiWβjJγΒMΘΔHεheΜTLαΣaΔoaΚwiZL7οβΝθΕcΘgGΠVNΨΠWzkiΒΑmJGCκηεΧΟΙbWQviWΞΓqhK4ςγΕξΗMΩeAδΒRΤjKΘrHεteΜT1υΣaτoaΚw4πZ7οΜ8ιηbΙGFΣΟWΞWUnigΔΓyNKAμγαβΗΑjeMΔSGζΤiΞqKβuYΖf3σΖgπQOΧΦ8θxtqnGΠA2τνWςγiΒK6μΗIδeCΩΚRΤbOzrXΝtmfD1υκΗτΦQΥQ4πusrq8θ40φσGφοΟV82τηiΒG4πΟIδW8θΚhΓbGΠYKβΝWΖjdΗΒgTPHεΧΤΜwovoab86ποΛκηYΜGEΥΟcΘWSriUΠΓulK2τγΑςΗEθe6μΣRΤTCΩrnwtOz91υξmτεCκI4πΧΚaP8θwYΜoGΠd7οΘWθjTΡΒGΠnHεxWΜj9νΒaδbHεΚKΜΘXΝdafbTΡΚΗnYQΥΝyteAμΗsβS0φΤMφΔpuh2τM4ςα4πξΒi98θεIδIGΠΛΙbaWjaWΞΛΓhaIδΛΕΚaMΩΛcΒaWΞΛkhaGζΛΕΞaMΩΛYΒfZΛΖkbQGζΦΛΞuYΜqYfd3σΘΗπUQΥΡ8θtlyrGΠD1υκWτΦiΒQ4πuIδq8θΚ3σbGπΠXΝV8θkeΖΑGΠRFηΥWΠsiΒsWjIχχδΓεΒOΧjJΚxHεncΜX9νΞaδgaΚΕKΘZNΨΜezcSΣΙmpWCκΟwΧi6πΓQκvJγpEΥΘ5ρdSμrTΡtCΩn1υxOτz9νl4πδDιJ8θΥΘcRGΠsUΠsWliχχΒΑΓz0φljφJDιδ2τΥΘcR4πsUΠs8θkχχzGηΑVΟkHΞjFηΒYΠfHεΖWΜjPΦΒavbHεΚqΜY4ςΝaξeaΚΗAδZRΤΜKΘrbΙteXT1υΣΟτogΔw4πN7οΩ8ιηzkGFΣΟEθWUΣnhΓxUnL9νβyδΕAμgKβΘNΨdMΔzTΡlinLDιβyΥΕAμgSβrNΨtMΔz1υliτLDιβ4πΥΔgR8θsMΩsGΠΑχχjWΟΒEθjXΣhHεΔUΜnLαxaΔb9νΚiδYKβΝKΘΖdΗfeUSPΦΤΣvqmxuqB53σςνπναLA8θγΓhKGΠΗKβeWΖjRΤΒgrPHεΧu