Base 53: 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
23 max steps10 → 0q → p1 → n3
327 max steps100 → 0qq → pq1 → oq2 → nq3 → mq4 → lq5 → kq6 → jq7 → iq8 → hq9 → gqA → fqB → eqC → dqD → cqE → bqF → aqG → ZqH → YqI → XqJ → WqK → VqL → UqM → TqN → SqO → RqP → QqQ
44 max stepsR000 → QqqQ → QPQR → 1qqp → p0p2
523 max stepsP0000 → OqqqS → SNqSP → T2qnO → oOqR3 → nPqQ4 → mNqS5 → lOqR6 → kMqT7 → jNqS8 → iLqU9 → hMqTA → gKqVB → fLqUC → eJqWD → dKqVE → cIqXF → bJqWG → aHqYH → ZIqXI → YGqZJ → aFqaH → bIqXG → aIqXH
6186 max stepsK000nn → nnJW34 → kjCd77 → dcQPEE → PO0pSS → p42nm2 → nlh854 → jgYHA8 → bWGZKG → LJBeXW → TEAfcO → VO4lSM → h93mhA → jYWJI8 → bGCdaG → RLJWVQ → DA0pge → pWQPK2 → nC0pe4 → pjRO72 → nc2nE4 → ljNS76 → fc4lEC → hTNSNA → X64lkK → heCdCA → XSQPOK → D40pme → piQP82 → na0pG4 → pjJW72 → ncCdE4 → jRNSP8 → b51olG → ngKVA4 → jWAfK8 → bVBeLG → TL9gVO → XA4lgK → hWCdKA → XRBePK → TD1odO → nQ4lQ4 → jgqq98 → ih2n99 → lZXIH6 → fIEbYC → TNFaTO → L64lkW → heAfCA → XVROLK → DA2nge → lWQPK6 → fC0peC → pTRON2 → n62nk4 → ljdC76 → fcQPEC → TO0pSO → p53ml2 → njfA74 → jcULE8 → bO8hSG → ZL3mVI → jH9gZ8 → bXHYJG → LHDcZW → PIAfYS → VG2naM → lK8hW6 → fZBeHC → USHYON → H73mja → jcIXE8 → bOEbSG → NL3mVU → jA6jg8 → dbVKFE → PMAfUS → V82niM → la8hG6 → fZJWHC → TICdYO → RG4laQ → hK0pWA → pXBeJ2 → nTDcN4 → jP5kR8 → fb1oFC → nTLUN4 → j95kh8 → fbXIFC → TMEbUO → N84liU → ha6jGA → dXJWJE → PECdcS → RO2nSQ → l40pm6 → pieB82 → naSNG4 → jK4lW8 → hbBeFA → XTLUNK → D95khe → fYQPIC → TG0paO → pK4lW2 → nhBe94 → jYSNI8 → bG4laG → hLJWVA → XD9gdK → XQCdQK → RCqqdQ → eQBeQD → TQqqPO → SR2nPP → l31on6 → nkeB64 → jeSNC8 → bS4lOG → hL3mVA → jX9gJ8 → bXDcJG → PLDcVS → PA2ngS → lW2nK6 → lfBeB6 → fUSNMC → T84liO → ha4lGA → hXJWJA → XECdcK → ROCdSQ → R40pmQ → pi0p82 → pnZG32 → nkIX64 → jeEbC8 → bSMTOG → L73mjW → jcAfE8 → bVNSLG → LA4lgW → hWAfKA → XVBeLK → TD9gdO → XQ4lQK → hCqqdA → ge3mCB → jVROL8 → bA2ngG → lWKVK6 → fCAfeC → VTRONM → 962nki → leYHC6 → fSGZOC → TJ3mXO → jE4lc8 → hbNSFA → XM4lUK → hD7idA → bXPQJG → LE0pcW → pOAfS2 → nV3mL4 → ki9g87 → daWJGE → PKCdWS → RC2neQ → lS0pO6 → pf3mB2 → njTM74 → jc6jE8 → dbNSFE → PM4lUS → h82niA → laWJG6 → fKCdWC → TRBePO → T51olO → ng4lA4 → jhVK98 → bYAfIG → VLFaVM
735 max steps200000Q → Q1qqqoR → pQOqRQ2 → oR0qpP3 → qmOqR41 → pmNqS42 → olOqR53 → njMqT74 → mgMqTA5 → lcJqWE6 → kXIqXJ7 → jSDqcO8 → iWDqcK9 → hVHqYLA → gQCqdQB → fUCqdMC → eTGqZND → dOBqeSE → fQEqbQC → eRAqfPD → gSEqbOB → fSCqdOC → eTEqbND → dQDqcQE → dPBqeRE → fQDqcQC → eSBqeOD → fRFqaPC → eQAqfQD → gSDqcOB → fTDqcNC → eSEqbOD → dQCqdQE → ePCqdRD → eRDqcPD → dRCqdPE
8158 max steps50000Ioo → ooI4lY23 → mlhFa955 → hgYKVIAA → XWGAfaKK → VKDBedWM → TQC8heQO → ZS4qqlOI → mYN6jTI5 → hdG5kaDA → fXQJWQJC → TECqqdcO → ecF8hbED → ZROLUSPI → H941omha → niYIXI84 → jaGEbaG8 → bNKJWWTG → LDC5kedW → fSQAfQOC → VT3qqmNM → nUP1oRM4 → nj81oi74 → njcZGE74 → jcOIXSE8 → bOF3mbSG → jML3mVU8 → jbA7igF8 → caWLUKGF → NKC8heWU → ZSC6jeOI → dSH3mZOE → jPI3mYR8 → jbG1oaF8 → nbMJWUF4 → jMD7idU8 → caQ7iQGF → bNJqqWTG → aXE2ncJH → lOJDcXS6 → fPE3mcRC → jTO1oSN8 → nb63mkF4 → kieLUC87 → daS8hOGE → ZPK3mWRI → jHC1oeZ8 → nbSHYOF4 → jMH3mZU8 → jbI7iYF8 → caMFaUGF → NLK7iWVU → bCA6jgeG → dWSKVOKE → PCB3mfeS → jUS2nOM8 → lb83miF6 → jfaLUGB8 → bUK8hWMG → ZLC7ieVI → bSH9gZOG → XLI3mYVK → jGD9gda8 → bXQJWQJG → LECqqdcW → ecI5kYED → fROFaSPC → TL41omVO → niA4lg84 → jhaVKG98 → bYKAfWIG → VLGBeaVM → TKA8hgWO → ZWC4leKI → hSHBeZOA → XTI3mYNK → jGD5kda8 → fbQJWQFC → TMCqqdUO → eUF0pbMD → pRM7iUP2 → nb81oiF4 → njaLUG74 → jcK8hWE8 → bZOBeSHG → TLI3mYVO → jGA4lga8 → hbWJWKFA → XMDBedUK → TQD7idQO → bQ4qqlQG → maLAfVG5 → hVK9gWLA → YWC9geKJ → XSFBebOK → TMD3mdUO → jQ84liQ8 → hbZqqGFA → gbR1oPFB → nVM1oUL4 → njA7ig74 → jcbVKFE8 → bOMAfUSG → VL83miVM → jaA8hgG8 → bZWJWKHG → LIDBedYW → TQGAfaQO → VK4qqlWM → mWP0pRK5 → phC1oe92 → omYROI43 → liG2na86 → lfaJWGB6 → fUKCdWMC → TRC7iePO → bS51olOG → ngL3mVA4 → kiW9gK87 → daXBeJGE → TPKDcWRO → PC51oleS → ngS2nOA4 → ljW3mK76 → jfcBeEB8 → bUTNSNMG → L864lkiW → heaAfGCA → XVSJWOLK → ECA3mged → jWSOROK8 → bC42nmeG → liSKVO86 → faB3mfGC → jUTJWNM8 → bD85kidG → faQKVQGC → TKAqqfWO → gWH2nZKB → lVIBeYL6 → fTG9gaNC → XTK5kWNK → fDC5kedC → fTSPQONC → T640pmkO → pie4lC82 → nhaROG94 → jYK2nWI8 → lbGBeaF6 → fTMJWUNC → TD85kidO → faQ4lQGC → hTJqqWNA → gXK2nWJB → lVEBecL6 → fTO9gSNC → XT63mkNK → jeD5kdC8 → fbSPQOFC