Base 57: 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 → 0u → t1 → r3
329 max steps100 → 0uu → tu1 → su2 → ru3 → qu4 → pu5 → ou6 → nu7 → mu8 → lu9 → kuA → juB → iuC → huD → guE → fuF → euG → duH → cuI → buJ → auK → ZuL → YuM → XuN → WuO → VuP → UuQ → TuR → SuS
44 max stepsT000 → SuuS → SRST → 1uut → t0t2
527 max steps10000 → 0uuuu → tuuu1 → t0ut2 → uqu31 → tqu32 → spu43 → rnu64 → qku95 → pguD6 → obuI7 → nVuO8 → mOuV9 → lNuWA → kNuWB → jMuXC → iMuXD → hLuYE → gLuYF → fKuZG → eKuZH → dJuaI → cJuaJ → bIubK → cGudJ → eJuaH → dKuZI → cIubJ
6145 max stepsH000SY → YSGdSN → NAuujY → kXAjNB → aY9kML → bFBifK → XQGdUO → N93qlY → ncAjI8 → fZJaLG → PHDgdW → TM6nYS → hC0tiE → tWSRO2 → r80tm4 → tndG72 → rgMXE4 → nSAjS8 → fYuuLG → eZ6nLH → hNDgXE → US9kSR → b2uurK → saFeK3 → pPFeV6 → jP5oVC → jX5oNC → jX9kNC → bX9kNK → bH9kdK → bMGdYK → NHBidY → XMAjYO → ZC8liM → dWChOI → VL7mZQ → fE4pgG → lSOVSA → b6uunK → oaBiK7 → hXFeNE → TP9kVS → b60toK → tiGdC2 → rWMXO4 → nB7mj8 → geXMGF → ROAjWU → Z82rmM → peChG6 → jVNWPC → X95olO → jc8lIC → dXJaNI → LH9kda → bMEfYK → RHBidU → XM2rYO → pC8li6 → jdVOHC → XM6nYO → hC8liE → dWSROI → L80tma → teEfG2 → rRNWT4 → n91sl8 → rfbIF4 → nQIbU8 → fJ3qbG → nPHcV8 → fL5oZG → jPDgVC → XT5oRO → j91slC → rcWNI4 → nK8la8 → fdFeHG → QOLYWV → D84pmi → leUPGA → bO4pWK → lH7mdA → fbLYJG → PIChcW → VK6naQ → hG4peE → lTNWRA → b91slK → rcGdI4 → nNJaX8 → fH9kdG → bPLYVK → HD5ohe → jUMXQC → XB3qjO → nY8lM8 → fdBiHG → XPLYVO → D95oli → jcUPIC → XK4paO → lG8leA → dbNWJI → LI8lca → dKEfaI → RLFeZU → PE2rgW → pS6nS6 → jguuDC → ih2rDD → pVTQP6 → j62roC → piWNC6 → jW8lOC → dX7mNI → fL9kZG → bPDgVK → TH5odS → jM0tYC → tXBiN2 → rX9kN4 → nb9kJ8 → fbHcJG → PLHcZW → LE6nga → hSEfSE → TQuuTS → URuuSR → TT1sRS → r20ts4 → tqm742 → rmeF84 → neOVG8 → fO6nWG → hP7mVE → fT5oRG → jP1sVC → rX5oN4 → nj9kB8 → fbXMJG → PIAjcW → ZK6naM → hGCheE → VTNWRQ → 951spm
736 max steps1000016 → 610uttp → usmu721 → tsku922 → sriuB33 → rpfuE54 → qmauJ85 → piSuRC6 → odGudH7 → nYLuYM8 → mSBuiS9 → lbFueJA → kWKuZOB → jQAujUC → kXIubNB → jSDugSC → iWDugOD → hVHucPE → gQCuhUF → iSFueSD → hTBuiRE → jUFueQC → iUDugQD → hVFuePE → gSEufSF → gRCuhTF → iSEufSD → hUCuhQE → iTGudRD → hSBuiSE → jUEufQC → iVEufPD → hUFueQE → gSDugSF → hRDugTE → hTEufRE → gTDugRF
8233 max stepsC0000HSY → YSHBidSN → XMAuujYO → kYL0tZMB → tZEBigL2 → rXSDgSN4 → nT9uukR8 → mlMGdY99 → dcNBiXII → XLK9kaZO → bGE8lgeK → dSOGdWSI → NL7uumZY → nZP0tVL8 → tfE5ogF2 → rjSPUSB4 → nY4uupM8 → qmTEfR85 → leR1sTGA → rbO1sWJ4 → rnI7mc74 → ngfJaFE8 → fSQGdUSG → PN3uuqXW → rXR0tTN4 → tnA1sk72 → sqgZKE43 → pmSEfS86 → jeQuuTGC → ieJAjbGD → ZVOHcWPM → LD85omha → jeUEfQGC → XRO3qWTO → n981sml8 → rfebIGF4 → nQOIbWU8 → fJ83qmbG → nePHcVG8 → fOL5oZWG → jPE7mgVC → fXS5oSNG → jP9uukVC → liLDgZCA → bWTDgROK → TH81smdS → reM0tYG4 → tnOBiW72 → rgX7mNE4 → nfS9kSF8 → fbPuuUJG → ebG6neJH → hONHcXWE → TLA7mkZS → faE0tgKG → tSPFeVS2 → rP5uuoV4 → qpSIbS55 → lkIuubAA → kkT8lRAB → daZ1sLKI → rLGDgeZ4 → nTODgWR8 → fT81smRG → reP1sVG4 → rnO5oW74 → njg7mEB8 → geYRSMGF → ROC0tiWU → tW82rmO2 → rpe7mG54 → nkfNWFA8 → faQ8lUKG → dPG3qeVI → nOL5oZW8 → jfE7mgFC → fXSPUSNG → PA4uupkW → qkQDgUA5 → laT3qRKA → nbG1seJ8 → rfOHcWF4 → nQL7mZU8 → geE3qgGF → nSRNWTS8 → f91uuslG → tlc5oI92 → rjcJaIB4 → nYKGdaM8 → fNGBieXG → XPO9kWVO → b985omlK → jecGdIGC → XONJaXWO → HA97mlke → fcaMXKIG → PKGAjeaW → ZOG6neWM → hOD7mhWE → fUT7mRQG → fP41sqVG → rmP5oV84 → nje5oGB8 → jfYNWMFC → XQC8liUO → dW93qlOI → ncL7mZI8 → geKDgaGF → TROFeWTS → P820tsmW → tqe6nG42 → rmhNWD84 → neU8lQG8 → fdO3qWHG → nPM7mYV8 → geC5oiGF → jWRNWTOC → X981smlO → rec8lIG4 → ndOJaWH8 → fMH7mdYG → fPMBiYVG → XPC5oiVO → jW95olOC → jcX7mNIC → fXK9kaNG → bPG9keVK → bOH5odWK → jMH7mdYC → fXMBiYNG → XPC9kiVO → bW95olOK → jcH7mdIC → fXMJaYNG → PHC9kidW → bWM6nYOK → hHC7midE → fWTLYROG → PD81smhW → reU6nQG4 → nhO3qWD8 → nfU7mQF8 → geQ3qUGF → nRO3qWT8 → nf81smF8 → rfePUGF4 → nQO4pWU8 → lf83qmFA → nebPUJG8 → fOI4pcWG → lPK7maVA → fbG5oeJG → jPOHcWVC → XL85omZO → jeE8lgGC → dXSNWSNI → LA8uulka → mkQ9kUA9 → dba3qKJI → nLIFecZ8 → fPKDgaVG → TPG5oeVS → jO60toWC → tiX7mNC2 → rfW9kOF4 → nbQ7mUJ8 → geI3qcGF → nROJaWT8 → fH81smdG → rePLYVG4 → nOD5ohW8 → jfU7mQFC → fXQ3qUNG → nPA3qkV8 → nfa5oKF8 → jfQFeUFC → XQP3qVUO → n963qol8 → nifbIFC8 → fWQIbUOG → PJ83qmbW → neI6ncG8 → hfOJaWFE → TQH7mdUS → fM40tqYG → tmPBiV82 → reX5oNG4 → njO9kWB8 → fbY7mMJG → fPIBicVG → XPK5oaVO → jG95oleC → jcXNWNIC → XKA8lkaO → daG8leKI → dOLFeZWI → PLE7mgZW → fSE6ngSG → hSOuuVSE → gWF2rfOF → pRQ7mUT6 → jf41sqFC → rmXPUN84 → neA4pkG8 → lfaNWKFA → bQG8leUK → dOH3qdWI → nML7mZY8 → geEBigGF → XSRNWTSO → A81uusml → tmi0tC82 → treVOG32 → roO6nW64 → nih7mDC8 → geWTQOGF → RO82rmWU → pe82rmG6 → pjeNWGB6 → jYO8lWMC → dXC7miNI → fWL9kZOG → bPE7mgVK → fSH5odSG → jPLuuYVC → iZK2raLD → pVGDgeP6 → jTO5oWRC → jX81smNC → reX9kNG4 → nbO9kWJ8 → fbI7mcJG → fPKHcaVG → PLG5oeZW