Base 71: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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
28 max steps10 → 0Ι → Θ1 → Ζ3 → Β7 → tFdVtF
338 max steps100 → 0ΙΙ → ΘΙ1 → ΗΙ2 → ΖΙ3 → ΕΙ4 → ΔΙ5 → ΓΙ6 → ΒΙ7 → ΑΙ8 → zΙ9 → yΙA → xΙB → wΙC → vΙD → uΙE → tΙF → sΙG → rΙH → qΙI → pΙJ → oΙK → nΙL → mΙM → lΙN → kΙO → jΙP → iΙQ → hΙR → gΙS → fΙT → eΙU → dΙV → cΙW → bΙX → aΙY → ZΙZYΙaZΙZ
439 max stepsa000 → ZΙΙZ → ZYZa → 1ΙΙΘ → Θ0Θ2ΘΕ32ΖΑ74ΒsF8tcVGd6ΒWv6ΒEvgREhEtSfEtUfAxUnAxMnQhMRGribGrYb2ΖYΔ2Ζ6ΔwB6xkNClMlOPMlkPKnkTKngTCvgjCvQjIpQXIpcX4Δcz4ΔAzoJApUdKV8zer8zIrYZIZ0ΘaΘ0Θ2
533 max stepsY0000 → XΙΙΙb → bWΙbY → c2ΙΖX → ΗXΙa3 → ΖYΙZ4 → ΕWΙb5 → ΔXΙa6 → ΓVΙc7 → ΒWΙb8 → ΑUΙd9 → zVΙcA → yTΙeB → xUΙdC → wSΙfD → vTΙeE → uRΙgF → tSΙfG → sQΙhH → rRΙgI → qPΙiJ → pQΙhK → oOΙjL → nPΙiM → mNΙkN → lOΙjO → kMΙlP → mLΙmN → nOΙjM → mOΙjNlNΙkOlMΙlOmMΙlNmOΙjN
6148 max steps9000RX → XR8zhc → rG4ΔsI → zcYZWA → p60ΘΓK → ΘwUdC2 → Ζk8zO4 → ΒrLmH8 → taQhYG → dH1ΗrW → Ζa6ΒY4 → Βv1ΗD8 → ΖthQF4 → ΒeGrU8 → tb9yXG → pd3ΕVK → ΒV7Αd8 → us7ΑGF → tfbWTG → dC4ΔwW → zk6ΒOA → vpLmJE → hWQhcS → HF5Γts → xeaXUC → lA2ΖyO → ΔoMlK6 → xUOjeC → lL9ynO → pSMlgK → VPDuje → hK8zoS → rUEteI → fZ9yZU → pAΙΙxK → yo7ΑKB → tnTeLG → dSAxgW → nE6ΒuM → vgQhSE → hHDurS → haEtYS → fF1ΗtU → ΖeAxU4 → Βn9yL8 → tpRgJG → dWEtcW → f75ΓΒU → xuAxEC → nlfSNM → ROCvki → jMGrmQ → bQIpiY → XI2Ζqc → ΔY4Δa6 → zx1ΗBA → ΖplMJ4 → ΒWOjc8 → tL5ΓnG → xdRgVC → lF7ΑtO → teMlUG → dP9yjW → pK6ΒoK → vVTedE → hB7ΑxS → tmEtMG → fdPiVU → JB7Αxq → tmWbMG → dQ4ΔiW → zI6ΒqA → vpXaJE → hW2ΖcS → ΔF5Γt6 → ywdUCB → nk8zOM → rRLmhI → ZRFsha → dG0ΘsW → Θc6ΒW2 → Ζv5ΓD4 → ΒxhQB8 → tmGrMG → dbPiXW → J73ΕΒq → ΒuWbE8 → tg4ΔSG → zdDuVA → ph7ΑRK → tVFsdG → ec7ΑWV → t95ΓzG → xqcVIC → lY6ΒaO → vN1ΗlE → ΖhNkR4 → ΒNFsl8 → tdNkVGdN7ΑlWtO6ΒkGvdLmVEhR7ΑhStGEtsGfdbWVUB84ΔΑyzsmLGApcQhWKVH5Γrexa8zYCrl1ΗNIΖZNkZ4ΒMΙΙl8ΑmFsM9rdPiVIZJ7ΑpatW0ΘcGΘd5ΓV2Ζx7ΑB4ΒtlMF8teOjUGdL9ynWpS6ΒgKvVDudEig7ΑSRtHDurGhdZYVSF80ΘΑuΘseTG2ΖcAxW4Βn5ΓL8xtRgFCleEtUOfN9ylUpOAxkKnVLmdMSQ7ΑihtIEtqGfdXaVUB82ΖΑyΔsmLG6xcQhWClH5ΓrOxaMlYClP1ΗjOΖNJol4ΒVNkd8tN7ΑlGtdNkVG
752 max stepsI00000I → IHΙΙΙqr → rqHΙqII → rZXΙaZI → qK0ΙΘoJ → ΙoVΙcK1 → ΘoIΙpK2 → ΗpUΙdJ3 → ΖnKΙnL4 → ΕlRΙgN5 → ΔhJΙoR6 → ΓkMΙlO7 → ΒgMΙlS8 → ΑfIΙpT9 → ziLΙmQA → yeLΙmUB → xdHΙqVC → wgKΙnSD → vcKΙnWE → ubGΙrXF → teJΙoUG → saJΙoYH → rZFΙsZI → taHΙqYG → scHΙqWH → rbJΙoXI → qYGΙraJ → sYHΙqaH → rbHΙqXI → rZIΙpZI → qZFΙsZJ → tZGΙrZG → sdHΙqVH → rbKΙnXI → qXFΙsbJ → tZIΙpZG → sbFΙsXH → tbKΙnXG → sZFΙsZH → tbIΙpXG → sbHΙqXH → rbIΙpXI → qZHΙqZJ → rXGΙrbI → sZJΙoZHrZEΙtZIubHΙqXFtdIΙpVGsbJΙoXHrZGΙrZIsZHΙqZHrbGΙrXIsZJΙoZH