Base 52: Cycles Sequences: All Cycle Counts

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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
21 cycle 1,326×(max) 26 nodes⮎ 0p → 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 24,752×(fixed) (max) 1 node ⮎ PpQ ⮌
43 cycles140,951×(max) 6 nodes⮎ C3le → iRN8 → a3lG → iJV8 → aBdG → SJVO ⮌
135,466×(max) 6 nodes⮎ KBdW → SBdO → S3lO → i3l8 → iZF8 → aJVG ⮌
64,586×3 nodes⮎ K3lW → iBd8 → aRNG ⮌
53 cycles2,533,028×3 nodes⮎ YFpZI → aGpYG → ZJpVH ⮌
1,283,982×(max) 4 nodes⮎ YGpYI → ZFpZH → aHpXG → ZIpWH ⮌
2,754×2 nodes⮎ QOpQQ → QpppP ⮌
64 cycles34,969,132×(max) 108 nodes⮎ 640olk → 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 ⮌
1,311,370×17 nodes⮎ E82mhc → kZNRG6 → eJ3lWC → iSCcN8 → aQ4kPG → gK0oVA → oWAeJ2 → mUCcL4 → iQ8gP8 → aY0oHG → oKGYV2 → mIAeX4 → iUEaL8 → aM8gTG → YK6iVI → cGAeZE → UOIWRM ⮌
6,996×2 nodes⮎ HF8gaZ → YLHXUI ⮌
702×(fixed) 1 node ⮎ QPppPQ ⮌
72 cycles254,745,460×(max) 19 nodes⮎ cOBpdRE → ePDpbQC → dRBpdOD → eQEpaPC → dQApePD → fRDpbOB → eSCpcNC → dSEpaND → cPCpcQE → dOCpcRD → dQDpbPD → cQBpdPE → ePCpcQC → dSCpcND → dQEpaPD → cPApeQE → fQCpcPB → eTCpcMC → dSFpZND ⮌
45,928,576×(fixed) 1 node ⮎ dQCpcPD ⮌
86 cycles832,498,927×113 nodes⮎ 8531nmki → mjfZFA64 → idVJVKC8 → aRCAedOG → URK2mVOM → kB82mhe6 → keZSMGB6 → eTJ5jWMC → eSD6icNC → cSP4kQNE → gO50okRA → ofW2mJA2 → mkVCcK54 → ifQAePA8 → aVU0oLKG → oKB8geV2 → mYTAeMH4 → iUH6iYL8 → caH8gYFE → YOLGYURI → IG92mgZY → kXJFZWI6 → eKFCcaVC → SQLAeUPO → U940olgM → ohX7hI82 → maZEaGF4 → iMLIWUT8 → aE96igbG → cXNJVSIE → OFC4kdaS → gRL3lUOA → iW92mgJ8 → kaXCcIF6 → eQLEaUPC → SM90ogTO → oX73liI2 → mibEaE74 → ibNLTSE8 → aN84khSG → gZK4kVGA → gWJAeWJA → WUDCccLK → QPC8gdQQ → YR0ppoOI → pXQ6iPI1 → ocF0oaD2 → omPKUQ32 → mjA0of64 → oidUKC72 → mbR9fOE4 → iWN2mSJ8 → kaD4kcF6 → gePKUQBA → WTA0ofMK → oVC6idK2 → mcRAeOD4 → iUP2mQL8 → ka90ogF6 → oeXKUIB2 → mTF9faM4 → iWL6iUJ8 → caD8gcFE → YPOKURQI → GA30omfa → ojVJVK62 → mdCAedC4 → iURQOOL8 → a931nmgG → mjXJVI64 → idFBdaC8 → aSRKUONG → KA52mkfW → kfVBdKA6 → eVSAeNKC → USB4keNM → gT84khMA → gZW6iJGA → cWJCcWJE → QODCccRQ → QP2ppmQQ → nQLppTP3 → mUO2mRL4 → ki92mg76 → kebWIEB6 → eTNDbSMC → SO74kiRO → gb42mlEA → khWMSJ86 → eZD5jcGC → eSPIWQNC → SE50okbO → ofN3lSA2 → miV4kK74 → igbAeE98 → aXUMSLIG → KF95jgaW → eXLBdUIC → TRF8gaON → YL62mjUI → kdG8gZC6 → eYRIWOHC → SHE2mbYO → kNH3lYS6 → ieH4kYB8 → gaTGYMFA → WLI6iXUK → cFC8gdaE → YROKUROI → GA32mmfa → kjVJVK66 → edCAedCC → USRQOONM ⮌
678,930,715×(max) 174 nodes⮎ A940olgg → 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 ⮌
630,050,081×73 nodes⮎ CA70oife → obVRNKE2 → mNB3leS4 → jhT4kM87 → gcZ6iGDA → cWPIWQJE → OED0ocbS → oPN3lSQ2 → mi50ok74 → oifaEA72 → mbVLTKE4 → iNB7heS8 → bZT4kMGF → gMJ6iWTA → cWD6icJE → cPOCcRQE → QO30omRQ → oj2ppm62 → nni2m723 → lljaE645 → hgdLTC99 → YXR7hOII → aGF2maZG → kLKIWVU6 → eEB8gebC → YTSMSNMI → G764kjia → gdbJVECA → WRNBdSOK → SC52mkdO → kfR3lOA6 → ieV2mKB8 → kaTAeMF6 → eUL6iULC → cS98ggNE → YXO4kRII → gGF2maZA → kWLIWUJ6 → eED8gcbC → YSPMSQNI → G650okja → ofdJVCA2 → mVRBdOK4 → iSB2meN8 → kaT4kMF6 → geL6iUBA → cWT8gMJE → YOD6icRI → cPG2mZQE → kOJ0oWR6 → oeD2mcB2 → mkTOQM54 → if71niA8 → mbaUKFE4 → iNL9fUS8 → aW94kgJG → gXKCcVIA → WQFAeaPK → ULC0odUM → oR97hgO2 → maX2mIF4 → kiLEaU76 → ebM8gTEC → YSN6iSNI → cG54kkZE → gfOIWRAA → WVE2mbKK → kNCAedS6 → eUR4kOLC → gS92mgNA → kXW4kJI6 → geFCcaBA → WTQKUPMK ⮌
59,396,871×38 nodes⮎ GDA6ifca → cVPJVQKE → OCB0oedS → oTR3lOM2 → mi72mi74 → kibaEE76 → ebNLTSEC → SN84khSO → gZ53lkGA → ifWIWJA8 → aVECcbKG → QNKAeVSQ → UB4ppkeM → leO9fRB5 → gWT2mMJA → kWD6icJ6 → ecPCcQDC → SQP0oQPO → o410ool2 → onmg8322 → mljXH644 → ihdFZC88 → aZRJVOGG → KJC2mdWW → kRDBdcO6 → eSP2mQNC → kS50okN6 → ofe4kBA2 → mgVSMK94 → iXB5jeI8 → eaTEaMFC → SML6iUTO → c973ligE → ibXNRIE8 → aNF3laSG → iLK4kVU8 → gaB8geFA → YWTKUMJI ⮌
16,567,689×11 nodes⮎ GED0ocba → oPNJVSQ2 → mC50okd4 → oifQOA72 → mbV1nKE4 → miNAeS74 → ibU4kLE8 → gaN8gSFA → YWL4kUJI → gGD8gcZA → YWPIWQJI ⮌
27,064×4 nodes⮎ HF98ggaZ → YXLHXUII → HFF8gaaZ → YLLHXUUI ⮌
97 cycles9,909,340,862×2 nodes⮎ gWK8pgVJA → hWNBpdSJ9 ⮌
3,253,874,490×(max) 14 nodes⮎ eUI8pgXLC → hUMBpdTL9 → gWI7phXJA → iXODpbRI8 → hVJ8pgWK9 → hYNBpdSH9 → gWMApeTJA → fWL9pfUJB → gUMApeTLA → fWJ7phWJB → iWMCpcTJ8 → hWJ9pfWJ9 → gYMCpcTHA → fULBpdULB ⮌
848,023,508×(fixed) 1 node ⮎ gWM9pfTJA ⮌
562,549,646×7 nodes⮎ fVI7phXKB → iWNCpcSJ8 → hWJ8pgWJ9 → hYNCpcSH9 → gVLApeUKA → fWK9pfVJB → gUMBpdTLA ⮌
206,867,748×6 nodes⮎ fWN9pfSJB → gUM8pgTLA → hWL7phUJ9 → iYOApeRH8 → hYN9pfSH9 → gYOApeRHA ⮌
2,485,652×(fixed) 1 node ⮎ hYP8pgQH9 ⮌
702×(fixed) 1 node ⮎ QQPpppPPQ ⮌
10+---Not showing digit sets 10+ due to verbosity.