Base 52: Cycles Sequences: Maximum Length Cycle Count

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
21 cycle 26 nodes0p → o1 → m3 → i7 → aF → KV → Af → UL → 8h → YH → GZ → IX → Eb → MT → 6j → cD → OR → 2n → k5 → eB → SN → 4l → g9 → WJ → Cd → QP
31 cycle (fixed) 1 node PpQ
43 cycles6 nodesKBdW → SBdO → S3lO → i3l8 → iZF8 → aJVG
53 cycles4 nodesYGpYI → ZFpZH → aHpXG → ZIpWH
64 cycles108 nodes640olk → ohdB82 → mZRNG4 → iJ3lW8 → iaCcF8 → aQKUPG → KA0ofW → oVBdK2 → mSAeN4 → iU4kL8 → ga8gFA → YWKUJI → GD9fca → WPJVQK → DB0oed → oTPPM2 → m6ppi4 → lj3l65 → igcC98 → aXPPIG → KEppaW → bV3lKF → iMAeT8 → aU6iLG → cK8gVE → YOAeRI → UG2mZM → kJ7hW6 → eaCcFC → SQKUPO → A40olg → ohVJ82 → mZBdG4 → iSIWN8 → aE4kbG → gNJVSA → WC4kdK → gRBdOA → WS2mNK → kC4kd6 → geQOBA → WT1nMK → mC6id4 → icQOD8 → aP1nQG → mK0oV4 → oiAe72 → mbTLE4 → iN7hS8 → bZ4kGF → gMIWTA → WE6ibK → cNBdSE → SO4kRO → g42mlA → khVJ86 → eZBdGC → TRIWON → E62mjc → kdNRC6 → eR3lOC → iS2mN8 → ka4kF6 → geKUBA → WT9fMK → WC6idK → cRBdOE → SO2mRO → k42ml6 → khdB86 → eZRNGC → SJ3lWO → iD3lc8 → iaOQF8 → aL1nUG → mK8gV4 → iYAeH8 → aUGYLG → KI8gXW → YFBdaI → SLFZUO → K93lgW → iXBdI8 → aSEaNG → MK4kVU → gB7heA → aWSMJG → KD5jcW → ePBdQC → TR0oON → o62mj2 → mkcC54 → ifPPA8 → aUppKG → ZV5jKH → eIAeXC → USEaNM → M84khU → gZ7hGA → aWIWJG → KECcbW → QNBdSQ → S4ppkO → lRHXO5 → gG2mZA → kWIWJ6 → eECcbC → SQMSPO
72 cycles19 nodescOBpdRE → ePDpbQC → dRBpdOD → eQEpaPC → dQApePD → fRDpbOB → eSCpcNC → dSEpaND → cPCpcQE → dOCpcRD → dQDpbPD → cQBpdPE → ePCpcQC → dSCpcND → dQEpaPD → cPApeQE → fQCpcPB → eTCpcMC → dSFpZND
86 cycles174 nodesA940olgg → ohXVJI82 → mZFBdaG4 → iSLIWUN8 → aE94kgbG → gXNJVSIA → WFC4kdaK → gRLBdUOA → WS92mgNK → kXC4kdI6 → geREaOBA → WTM2mTMK → kC76iid6 → ecbQOEDC → SPN1nSQO → m540olk4 → oiheA872 → mbZTLGE4 → iNJ7hWS8 → bZD4kcGF → gPMIWTQA → WE70oibK → obNBdSE2 → mSN4kSN4 → ig54kk98 → gfaWIFAA → WVLDbUKK → OCB8gedS → YTR3lOMI → iG72miZ8 → kbaIWFE6 → eNLDbUSC → SO94kgRO → gX42mlIA → khWEaJ86 → eZMCcTGC → SQJ6iWPO → cD40olcE → ohPNRQ82 → mZ40olG4 → oihIW872 → mbZDbGE4 → iONIWSR8 → aE52mkbG → kfNJVSA6 → eVC4kdKC → gSRAeONA → WU52mkLK → kfC8gdA6 → eYVQOKHC → SHB1neYO → mTH3lYM4 → jhH6iY87 → dbZGYGED → QNJHXWSQ → GD4ppkca → lcU1nLD5 → mgP8gQ94 → iYX0oIH8 → oaHEaYF2 → mMLGYUT4 → iI96igX8 → caXEaIFE → OMLEaUTS → M973ligU → ibX7hIE8 → bZNEaSGF → NLJ4kWUT → gD95jgcA → eXWOQJIC → SFD1ncaO → mPL3lUQ4 → jh90og87 → ocZWIGD2 → mPJDbWQ4 → iOD0ocR8 → oaP2mQF2 → mkL0oU54 → oif8gA72 → mbYUKHE4 → iNH9fYS8 → aWH4kYJG → gKHCcYVA → WQHAeYPK → UHC0odYM → oRH7hYO2 → maH2mYF4 → kiLGYU76 → ebI8gXEC → YSNEaSNI → MG54kkZU → gfJ7hWAA → aWVCcKJG → QKDAecVQ → UPAppeQM → fTF3laMB → iUL6iUL8 → ca98ggFE → YXOKURII → GFA2mfaa → kVLJVUK6 → eCB8gedC → YTSQONMI → G751nkia → mfbJVEA4 → iVNBdSK8 → aSB4keNG → gTK4kVMA → gWB6ieJA → cWTCcMJE → QOD6icRQ → cP2ppmQE → nbNBdSE3 → kSN4kSN6 → ge54kkBA → gfWSMJAA → WVD5jcKK → ePCAedQC → USR0oONM → o852mkh2 → mkfYGA54 → ifVHXKA8 → aVGAeZKG → UKJAeWVM → UDB7hecM → aTP7hQMG → aK70oiVG → obKAeVE2 → mUNAeSL4 → iU94kgL8 → gaX8gIFA → YWLEaUJI → MGD8gcZU → YPJ7hWQI → aGD0ocZG → oPKIWVQ2 → mEB0oeb4 → oiTMSM72 → mb75jiE4 → iebMSEB8 → aTN5jSMG → eK74kiVC → gbSAeNEA → WUN4kSLK → gC94kgdA → gXWQOJIA → WFD1ncaK → mPLBdUQ4 → iS90ogN8 → oaX4kIF2 → mgLEaU94 → iXM8gTI8 → aYF6iaHG → cLKGYVUE → OIB8geXS → YTF3laMI → iLG6iZU8 → caJ8gWFE → YOLCcURI → QG92mgZQ → kXIppWI6 → jXS0oNI7 → ocF4kaD2 → mgPKUQ94 → iXA0ofI8 → oaVEaKF2 → mMLAeUT4 → iU96igL8 → caX8gIFE → YOLEaURI → MG92mgZU → kXJ7hWI6 → eaFCcaFC → SQLKUUPO
97 cycles14 nodeseUI8pgXLC → hUMBpdTL9 → gWI7phXJA → iXODpbRI8 → hVJ8pgWK9 → hYNBpdSH9 → gWMApeTJA → fWL9pfUJB → gUMApeTLA → fWJ7phWJB → iWMCpcTJ8 → hWJ9pfWJ9 → gYMCpcTHA → fULBpdULB