Base 97: 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
224 max steps10 → 0λ → κ1 → θ3δ7ΥFΔVbxrhΠJvdzZjpΩBΜNnlθ3
351 max steps100 → 0λλ → κλ1 → ιλ2 → θλ3 → ηλ4 → ζλ5 → ελ6 → δλ7 → γλ8 → βλ9 → αλA → ΩλB → ΨλC → ΧλD → ΦλE → ΥλF → ΤλG → ΣλH → ΡλI → ΠλJ → ΟλK → ΞλL → ΝλM → ΜλN → ΛλO → ΚλP → ΙλQ → ΘλR → ΗλS → ΖλT → ΕλU → ΔλV → ΓλW → ΒλX → ΑλY → zλZ → yλa → xλb → wλc → vλd → uλe → tλf → sλg → rλh → qλi → pλj → oλk → nλl → mλmlλnmλm
428 max stepsn000 → mλλm → mlmn → 1λλκ → κ0κ2κη32θγ74δΤF8ΥΓVGΔWΒWXUΔΓZUΔΑZQΘΑhQΘshAΩsΞAΩMΞqhMr8βiΣ8βIΣyZIzOΚalOΚol2θoζ2θ6ζΨB6ΩΛNCΜmlOn0κmκ0κ2
543 max steps10000 → 0λλλλ → κλλλ1 → κ0λκ2 → ληλ31 → κηλ32 → ιζλ43 → θδλ64 → ηαλ95 → ζΦλD6 → εΠλI7 → δΚλO8 → γΓλV9 → βuλdA → αlλmB → ΩcλvC → ΨkλnD → ΧbλwE → ΦjλoF → ΥaλxG → ΤiλpH → ΣZλyI → ΡhλqJ → ΠYλzK → ΟgλrL → ΞXλΑM → ΝfλsN → ΜWλΒO → ΛeλtP → ΚVλΓQ → ΙdλuR → ΘUλΔS → ΗcλvT → ΖTλΕU → ΖaλxU → ΕUλΔV → ΕYλzV → ΔVλΓW → ΔWλΒW → ΓWλΒX → ΓUλΔXΕVλΓVΔYλzWΓUλΔX
6223 max stepsT000ΧΧ → ΧΧSΖDE → ΙΘcvRR → hgIΠss → xCAΩΨc → ΞΛKΞOM → trlmhg → DA0καΨ → κΟΙPK2 → θuipe4 → δG6δΤ8 → ΧΥΒWFE → ΘΕUΔUS → faYzyu → ROEΥΛΙ → ΖmgrmU → bAλλΩy → αxOΚbB → ΞlLΝnM → sq1ιih → θB7γΩ4 → δΥΜMF8 → ΥΕojUG → Δa4ζyW → βXNΛΒA → ΠnTΕlK → vb1ιxe → θMGΣΝ4 → δΒpiX8 → ΥU6δΕG → ΧΔZyVE → ΘYOΚΑS → lfRΗto → fE2θΦu → ζΗEΥS6 → ΩΖduTC → ΜcGΣwO → ΒnJΟlY → vT1ιΖe → θcGΣw4 → δΒJΟX8 → ΥvTΕdG → ΔbHΡxW → zXLΝΒa → rUOΚΕi → la8βyo → ΣO2θΛI → ζzlmZ6 → ΩQ0κΙC → κΜhqN2 → θo8βk4 → δΣ3ηH8 → δΥzYF8 → ΥΕQΘUG → ΔhZyrW → XP9αΚΓ → ΠkUΔoK → vZ3ηze → δQGΣΙ8 → ΥΒhqXG → ΔU8βΕW → ΣaWΒyI → zVNΛΔa → nYOΚΑm → lS0κΗo → κe2θu2 → θζFΤ54 → δαΓVA8 → ΥΟWΒKG → ΔuUΔeW → ZXFΤΒΑ → ΔUQΘΕW → haWΒys → VOAΩΛΕ → ΞmYzmM → rQλλΘi → ΙqFΤiR → Δh7γrW → ΥX9αΒG → ΠΔTΕVK → vbXΑxe → TMGΣΝΗ → ΒqcviY → TJ7γΠΗ → ΥwcvcG → ΔKIΠΟW → xuWΒec → VLFΤΞΕ → ΔsYzgW → XRBΨΘΓ → ΜgUΔsO → nZBΨzm → ΜQ0κΙO → κnhql2 → θ91ιβ4 → θδΠI74 → δΦwbE8 → ΥΗKΞSG → ΔtdufW → XHDΦΣΓ → ΘΑUΔYS → fZRΗzu → fQEΥΙu → ΖiEΥqU → Ζb7γxU → ΥbLΝxG → ΔrLΝhW → rX9αΒi → ΠU8βΕK → ΣvZydI → zPHΡΚa → zkOΚoa → lP3ηΚo → δk2θo8 → ζΥ3ηF6 → δΩΔUB8 → ΥΝYzMG → ΔqQΘiW → hX7γΒs → ΥUAΩΕG → ΞΔZyVM → rYOΚΑi → lS8βΗo → Σe2θuI → ζzFΤZ6 → ΩΔPΙVC → ΜjXΑpO → nT5εΖm → Ωc0κwC → κΜJΟN2 → θvnkd4 → δI2θΡ8 → ζΥxaF6 → ΩΕMΜUC → ΜpZyjO → nP5εΚm → Ωk0κoC → κΜ3ηN2 → θδnk74 → δΦ2θE8 → ζΥΖSF6 → ΩΕcvUC → ΜaIΠyO → xnNΛlc → nL1ιΞm → θs0κg4 → κδBΨ72 → θΦΛNE4 → δΗmlS8 → Υe0κuG → κΔFΤV2 → θΔXΑV4 → δYSΖΑ8 → ΥdRΗvG → ΔfHΡtW → zXDΦΒa → ΘUOΚΕS → lfZyto → PE2θΦΛ → ζΗknS6 → Ωe2θuC → ζΜFΤN6 → ΩΔnkVC → ΜY2θΑO → ζnRΗl6 → Ωf1ιtC → θΜDΦN4 → δΘnkR8 → Υg2θsG → ζΔBΨV6 → ΩΜXΑNC → ΜoSΖkO → nd3ηvm → δI0κΡ8 → κΥxaF2 → θΕMΜU4 → δpZyj8 → ΥP5εΚG → ΩΔjoVC → ΜY4ζΑO → βnRΗlA → Πf1ιtK → θvDΦd4 → δΘHΡR8 → ΥzfsZG → ΔQCΧΙW → ΚiWΒqQ → jV7γΔq → ΥY6δΑG → ΧΔRΗVE → ΘfXΑtS → fTDΦΖu → ΘcEΥwS → ΖfJΟtU → vbDΦxe → ΘMGΣΝS → ΒqetiY → TF7γΥΗ → ΥΕcvUG → ΔaIΠyW → xXNΛΒc → nUKΞΕm → ta0κyg → κOCΧΛ2 → θΚlmP4 → δk0κo8 → κΥ3ηF2 → θδΔU74 → δΦYzE8 → ΥΗQΘSG → ΔhdurWXH9αΣΓΠΑUΔYKvZRΗzefQGΣΙuΒiEΥqYΖT7γΖUΥcaxwGΔNJΟΜWvoWΒkeVH3ηΣΕδΑYzY8ΥSQΘΗGΔhdurW
749 max steps1000012 → 210λκκκ → λιηλ321 → κιελ522 → ιθγλ733 → θζΩλA54 → ηγΤλF85 → ζΨΛλNC6 → εΣyλZH7 → δΜhλqN8 → γΕTλΕU9 → βxZλybA → αqMλΜiB → ΩΓSλΖWC → ΨvYλzdD → ΧoLλΝkE → ΦΑRλΗYF → ΥtXλΑfG → ΤmKλΞmH → ΣyQλΘaI → ΡrWλΒhJ → ΠkJλΟoK → ΠvTλΕdK → ΟmQλΘmL → ΞoKλΞkM → ΟrSλΖhL → ΞmNλΛmM → ΝqNλΛiN → ΜpRλΗjO → ΛkMλΜoP → ΝmPλΙmN → ΜnLλΝlO → ΞoPλΙkM → ΝoNλΛkN → ΜpPλΙjO → ΛmOλΚmP → ΛlMλΜnP → ΝmOλΚmN → ΜoMλΜkO → ΝnQλΘlN → ΜmLλΝmO → ΞoOλΚkM → ΝpOλΚjN → ΜoPλΙkO → ΛmNλΛmP → ΜlNλΛnO → ΜnOλΚlO → ΛnNλΛlPΜlOλΚnOΛnNλΛlP