Base 54: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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
Cycle Start
11 max steps10
22 max steps20 → 1q → o3
328 max steps100 → 0rr → qr1 → pr2 → or3 → nr4 → mr5 → lr6 → kr7 → jr8 → ir9 → hrA → grB → frC → erD → drE → crF → brG → arH → ZrI → YrJ → XrK → WrL → VrM → UrN → TrO → SrP → RrQ → QrR
47 max steps700K → K6kY → eDdE → ROSR → 3rro → o2o4 → mj76 → gbFC
526 max steps30000 → 2rrrp → p1rp3 → qlr52 → pkr63 → oir84 → nfrB5 → mbrF6 → lWrK7 → kQrQ8 → jJrX9 → iPrRA → hIrYB → gOrSC → fHrZD → eNrTE → dGraF → cMrUG → bFrbH → cJrXG → bIrYH → aIrYI → ZHrZJ → aFrbI → cIrYG → bJrXH → aHrZI
6170 max steps3000Ih → hI2oZB → mWGaL6 → gKAgXC → WUCeNM → SA6khQ → eX1pKE → oQCeR4 → kS0qP8 → qc2oF2 → omMU54 → kh7jA8 → dbWKGF → OLBfWU → UB5lgO → gV5lMC → gU8iNC → aU6kNI → eI6kZE → eQGaRE → QK0qXS → qD1pe2 → pnQQ43 → mirr86 → lj3n87 → keaGD8 → cRJXQG → ME0qdW → qP9hS2 → oY2oJ4 → mkEc76 → gdNTEC → UP5lSO → g62olC → mfTNC6 → gT5lOC → gU4mNC → iU6kNA → eY6kJE → eQEcRE → QO0qTS → q51pm2 → pngA43 → mjVL86 → gb9hGC → YUKWNK → EC6kfe → eTPROE → Q51pmS → oh1pA4 → okWK74 → kdBfE8 → cUOSNG → M73nkW → kd9hE8 → cYOSJG → MF3ncW → kN9hU8 → cY6kJG → eMEcVE → QO8iTS → a51pmI → ohHZA4 → kXHZK8 → cICeZG → SMGaVQ → K91piY → oZDdI4 → kQGaR8 → cK0qXG → qMCeV2 → oS8iP4 → ka2oH8 → mcIYF6 → gNFbUC → UM6kVO → e95liE → gZPRIC → UH1paO → oJ5lY4 → kgEcB8 → cVNTMG → M95liW → gZ9hIC → YUGaNK → KE6kdY → ePDdSE → RP2oSR → m2rro6 → pl1p63 → omeC54 → khRPA8 → cX1pKG → oMCeV4 → kS8iP8 → ca2oHG → mMIYV6 → gG8ibC → aUKWNI → IC6kfa → eTHZOE → QI4mZS → iH1paA → oYIYJ4 → kGEcb8 → cOKWTG → MC4mfW → iT9hOA → ZX4mKJ → iGCebA → YSKWPK → EC2ofe → mTPRO6 → g51pmC → ohTNA4 → kX5lK8 → gcCeFC → USMUPO → 862olk → mfbFC6 → gTLVOC → UA4mhO → iX5lKA → gYCeJC → USEcPO → O62olU → mf5lC6 → hfSOCB → WT3nOM → kA4mh8 → icWKFA → YNBfUK → UE6kdO → eP5lSE → gQ2oRC → mU0qN6 → qg6kB2 → oeUMD4 → kR7jQ8 → db0qGF → qOKWT2 → oC4mf4 → kiSO98 → cZ3nIG → kMGaV8 → cK8iXG → aMCeVI → SI8iZQ → aH1paI → oJHZY4 → kIEcZ8 → cOGaTG → MK4mXW → iD9heA → ZXQQKJ → GCrrec → fb1pGD → oSKWP4 → kC2of8 → mcSOF6 → gN3nUC → kU6kN8 → ec6kFE → eQMURE → Q80qjS → qb1pG2 → pnKW43 → mjBf86 → gbTNGC → UL5lWO → gB5lgC
730 max stepsR00000q → qQrrrQ2 → pRQrQQ3 → oP0rqS4 → rmOrS51 → qmNrT52 → plOrS63 → ojMrU84 → ngMrUB5 → mcJrXF6 → lXIrYK7 → kTDrdO8 → jXErcK9 → iVHrZMA → hRCreQB → gVDrdMC → fTGraOD → ePBrfSE → gRErcQC → fSBrfPD → gSFrbPC → fRBrfQD → gSErcPC → fSCrePD → fSErcPD → eRCreQE → fQDrdRD → eSCrePE → fQErcRD → eRBrfQE → gRDrdQC
8301 max steps50000FFl → lFF4mcc7 → ieNMUUDA → YR86kjQK → ebE0qdGE → qQPKWSR2 → oC30qof4 → qlkSO762 → ofd3nEC4 → ljTOSO87 → eb53nmGE → khQKWRA8 → cXC0qfKG → qTMCeVO2 → oS94miP4 → kiZ2oI98 → mcZGaIF6 → gNKGaXUC → UKD6keXO → eRD5leQE → gRQ0qRQC → qU10qqN2 → qpo6k322 → onldD644 → kjfPRC88 → cbT1pOGG → oML4mWV4 → kiB8ig98 → caZUMIHG → MJH7jaYW → cJF9hcYG → YNMEcVUK → OE96kidU → eZP5lSIE → gQH2oaRC → mUJ0qYN6 → qgF6kcB2 → oeVMUMD4 → kR97jiQ8 → dbZ0qIGF → qOLGaWT2 → oKB4mgX4 → kiVCeM98 → cZS8iPIG → aMH2oaVI → mJI8iZY6 → gaHEcaHC → UOJIYYTO → GF64mlcc → ifNLVUCA → YTA6khOK → eXE4mdKE → iQPCeSRA → YS30qoPK → qlE2od62 → omfOSC54 → khT3nOA8 → kcX4mKF8 → icNCeUFA → YSN6kUPK → eE72okdE → mdQOSRE6 → gP40qnSC → qjU2oN82 → omb6kG54 → kheKWDA8 → cXRBfQKG → UMD0qeVO → qR95liQ2 → ogZ0qIB4 → qkVGaM72 → odK8iXE4 → kaPCeSH8 → cSJ2oYPG → mMF2ocV6 → mgN8iUB6 → gaV6kMHC → eUJ8iYNE → aQF6kcRI → eNI0qZUE → qQH6kaR2 → oeJ0qYD4 → qkREcQ72 → odO0qTE4 → qkP4mS72 → oid2oE94 → mkZOSI76 → gdH3naEC → kUPIYSN8 → cG72okbG → mdMKWVE6 → gPC8ifSC → aUT2oONI → mI74mkZ6 → igdGaEBA → YVPJXSMK → FD92oied → mZRNTQI6 → gH60qlaC → qfUIYNC2 → oTG6kbO4 → keL4mWD8 → icRAgQFA → YWN0qULK → qEB6kgd2 → oeVOSMD4 → kR93niQ8 → kcZ0qIF8 → qcNGaUF2 → oNK6kXU4 → keD6keD8 → ecRQQQFE → QN0rrqUS → rUQ1pRN1 → qo70qk32 → qolcE632 → olfNTC64 → kfT5lOC8 → gcT4mOFC → iUN4mUNA → iY76kkJA → edYEcJEE → QPOEcTSS → O531pomU → olh5lA64 → kgfWKCB8 → cVTBfOMG → UM94miVO → iZ95liIA → gZYGaJIC → UKHEcaXO → OJD5leYU → gRF5lcQC → gUN0qUNC → qU76kkN2 → oed6kED4 → keROSQD8 → cR40qnQG → qjM0qV82 → qob8iG32 → olaKWH64 → kfJBfYC8 → cUTEcONG → OM74mkVU → id95liEA → gZYOSJIC → UHF3ncaO → kNJ5lYU8 → gcF6kcFC → eUNMUUNE → Q876kkjS → edb1pGEE → oQPKWSR4 → kC30qof8 → qlcSOF62 → ofN3nUC4 → ljT6kO87 → fdb4mGED → iSPKWSPA → YC32oofK → mlTDdO66 → gfQ4mRCC → iUT0qONA → qY74mkJ2 → oidEcE94 → kZPNTSI8 → cH62olaG → mfMIYVC6 → gTG8ibOC → aUL4mWNI → iIB6kgZA → eYVGaMJE → QKF8icXS → aND1peUI → oRI6kZQ4 → keH0qaD8 → qcRIYQF2 → oNG0qbU4 → qkL6kW72 → oedAgED4 → kWROSQL8 → cB40qngG → qjVLVM82 → obA8ihG4 → kaXKWKH8 → cJDBfeYG → URMEcVQO → O960qliU → qfZ5lIC2 → ogTGaOB4 → kVK4mXM8 → icD8ieFA → aYRMUQJI → IF80qjca → qbNHZUG2 → oLI6kZW4 → keHAgaD8 → cWRIYQLG → MGB0qgbW → qVL9hWM2 → oYB8igJ4 → kaVEcMH8 → cOJ8iYTG → aMF4mcVI → iNI8iZUA → aYH6kaJI → eJIEcZYE → QOHEcaTS → OJ51pmYU → ohF5lcA4 → kgXMUKB8 → cVD7jeMG → cRM8iVQG → aM90qiVI → qZI8iZI2 → oaHGaaH4 → kKJIYYX8 → cGFCecbG → SNMKWVUQ → C971pkig → odZTNIE4 → kPH5laS8 → gcJ2oYFC → mUNEcUN6 → gO76kkTC → edU4mNEE → iQP6kSRA → eY30qoJE → qlQEcR62 → ofO0qTC4 → qkT4mO72 → oid4mE94 → kiZOSI98 → cZH3naIG → kMJGaYV8 → cKF8icXG → aNMCeVUI → SI96kiZQ → eZH1paIE → oQJGaYR4 → kKF0qcX8 → qcNCeUF2 → oSN6kUP4 → ke72okD8 → mdcQQFE6 → gPMrrUSC → fVH1paMD → oSJ8iYP4 → kaF2ocH8 → mcNIYUF6 → gNG6kbUC → eUL6kWNE → eQB6kgRE → eVQ0qRME → qQ90qiR2 → qoZ0qI32 → qolGa632 → olfJXC64 → kfTDdOC8 → cTQ4mROG → iM50qmVA → qhY8iJA2 → oaXEcKH4 → kOJCeYT8 → cSF4mcPG → iNM2oVUA → mY96kiJ6 → geZEcIDC → UROGaTQO → K650qmlY → qhfDdCA2 → oXTPROK4 → kD51pme8 → ohcQQFA4 → kXMrrUK8 → jXO2oTK9 → maD4meH6 → igRIYQBA → YVG0qbMK → qLE8idW2 → oaPAgSH4 → kWJ2oYL8 → mcFAgcF6 → gWNMUULC → UB86kjgO → ebV5lMGE → gQL8iWRC → aUB0qgNI → qVI6kZM2 → oeH8iaD4 → kaRIYQH8 → cJG0qbYG → qMLEcWV2 → oOB8igT4 → kaV4mMH8 → icJ8iYFA → aYNEcUJI → OIF6kcZU → eNH5laUE → gQJ6kYRC → eUF0qcNE → qQN6kUR2