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 steps1 → 0 → 0
28 max steps10 → 0Ι → Θ1 → Ζ3 → Β7 → tF → dV → 7Β → tF
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 → ZΙZ → YΙa → ZΙZ
439 max stepsa000 → ZΙΙZ → ZYZa → 1ΙΙΘ → Θ0Θ2 → ΘΕ32 → ΖΑ74 → ΒsF8 → tcVG → d6ΒW → v6ΒE → vgRE → hEtS → fEtU → fAxU → nAxM → nQhM → RGri → bGrY → b2ΖY → Δ2Ζ6 → ΔwB6 → xkNC → lMlO → PMlk → PKnk → TKng → TCvg → jCvQ → jIpQ → XIpc → X4Δc → z4ΔA → zoJA → pUdK → V8ze → r8zI → rYZI → Z0Θa → Θ0Θ2
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 → mOΙjN → lNΙkO → lMΙlO → mMΙlN → mOΙjN
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 → tdNkVG → dN7ΑlW → tO6ΒkG → vdLmVE → hR7ΑhS → tGEtsG → fdbWVU → B84ΔΑy → zsmLGA → pcQhWK → VH5Γre → xa8zYC → rl1ΗNI → ΖZNkZ4 → ΒMΙΙl8 → ΑmFsM9 → rdPiVI → ZJ7Αpa → tW0ΘcG → Θd5ΓV2 → Ζx7ΑB4 → ΒtlMF8 → teOjUG → dL9ynW → pS6ΒgK → vVDudE → ig7ΑSR → tHDurG → hdZYVS → F80ΘΑu → ΘseTG2 → ΖcAxW4 → Βn5ΓL8 → xtRgFC → leEtUO → fN9ylU → pOAxkK → nVLmdM → SQ7Αih → tIEtqG → fdXaVU → B82ΖΑy → ΔsmLG6 → xcQhWC → lH5ΓrO → xaMlYC → lP1ΗjO → ΖNJol4 → ΒVNkd8 → tN7ΑlG → tdNkVG
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 → sZJΙoZH → rZEΙtZI → ubHΙqXF → tdIΙpVG → sbJΙoXH → rZGΙrZI → sZHΙqZH → rbGΙrXI → sZJΙoZH