Base 46: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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 → 1i → g3
324 max steps100 → 0jj → ij1 → hj2 → gj3 → fj4 → ej5 → dj6 → cj7 → bj8 → aj9 → ZjA → YjB → XjC → WjD → VjE → UjF → TjG → SjH → RjI → QjJ → PjK → OjL → NjM → MjN
47 max steps600H → H5dT → YBXC → NKON → 3jjg → g2g4 → eb76 → YTFC
521 max steps10000 → 0jjjj → ijjj1 → i0ji2 → jfj31 → ifj32 → hej43 → gcj64 → fZj95 → eVjD6 → dQjI7 → cKjO8 → bHjR9 → aJjPA → ZGjSB → YIjQC → XFjTD → WHjRE → VEjUF → VFjTF → UFjTG → UDjVG
6163 max stepsA000AN → NA9ZZN → QOjjKK → PP1hKL → g53fe4 → dbYA87 → WTNLGE → ID1hWS → gJ9ZQ4 → cQ6cJ8 → WU6cFE → WIEURE → IG8aTS → SD9ZWI → QJ9ZQK → Q75dcK → YV5dEC → YMGSNC → MC0iXO → iL1hO2 → hf2g43 → fda865 → aXRHCA → QL9ZOK → Q62gdK → eX5dC6 → ZXKOCB → OL3fOM → c31hg8 → gdTF64 → cXDVC8 → ULHROG → EA2gZW → ePHRK6 → YA4eZC → aPLNKA → Q51heK → gZ5dA4 → cYOKB8 → UN3fMG → cE0iV8 → iUGSF2 → gFBXU4 → cMEUN8 → UG0iTG → iECWV2 → gKGSP4 → cC4eX8 → aUKOFA → QF3fUK → cF5dU8 → YUEUFC → MGEUTO → GD1hWU → gJDVQ4 → cI6cR8 → WU8aFE → SIEURI → GA8aZU → SPDVKI → IA4eZS → aP9ZKA → RP4eKJ → a84ebA → aTPJGA → QD5dWK → YJ5dQC → YM6cNC → WM0iNE → iI0iR2 → ig8a32 → gdRH64 → cX9ZC8 → UQKOJG → E73fcW → cVHRE8 → UH9ZSG → QEAYVK → OH5dSM → YB1hYC → gNLNM4 → c20ih8 → ifTF42 → gbDV84 → cTHRG8 → UD9ZWG → QJDVQK → I75dcS → YV9ZEC → QMGSNK → C60idY → iXLNC2 → gL1hO4 → gc2g74 → ecUE76 → YVFTEC → MHDVSO → IB1hYS → gN9ZM4 → cQ0iJ8 → iU6cF2 → gWEUD4 → cJFTQ8 → UE6cVG → WHDVSE → JHAYSR → OB7bYM → UN1hMG → gE0iV4 → icGS72 → gVBXE4 → cMGSN8 → UC0iXG → iLDVO2 → gI2gR4 → ec8a76 → YVRHEC → MH9ZSO → QB1hYK → gN5dM4 → cY0iB8 → iUMMF2 → gEjjU4 → fVBXE5 → aMGSNA → QC0iXK → iL5dO2 → gY2gB4 → ecMM76 → YUjjEC → XV3fED → cKGSP8 → UC4eXG → aLDVOA → QI2gRK → e95da6 → ZXQICB → OL7bOM → U31hgG → gdDV64 → cXHRC8 → UL9ZOG → QE2gVK → eH5dS6 → ZXAYCB → PNKOML → 530igf → idZ962 → gXPJC4 → cL5dO8 → YU2gFC → eMEUN6 → YG0iTC → iMCWN2 → gK0iP4 → ic4e72 → gaUE94 → cRFTI8 → UE8aVG → SHDVSI → IB9ZYS → QN9ZMK → Q60idK → iX5dC2
728 max steps800000N → N7jjjbN → cMLjNN8 → bH0jiS9 → jZJjPA1 → iZFjTA2 → hYJjPB3 → gWEjUD4 → fTHjRG5 → ePBjXK6 → dTCjWG7 → cRFjTI8 → bNAjYM9 → aRBjXIA → ZPEjUKB → YL9jZOC → aNCjWMA → ZO9jZLB → aODjVLA → ZN9jZMB → aOCjWLA → ZOAjYLB → ZOCjWLB → YNAjYMC → ZMBjXNB → YOAjYLC → ZMCjWNB → YN9jZMC → aNBjXMA
8164 max steps70000Hff → ffH6cS45 → baWAYD99 → SROIQLII → A982gbaa → eTRPJIG6 → YD95daWC → YRMIQNIC → M980ibaO → iTR1hIG2 → hfD8aW43 → ebSIQH86 → YTB7bYGC → UNMCWNMG → KE10iiVQ → ihH5dS22 → gfYAYB44 → cbOMML88 → UT2jjgGG → hTQ0iJG3 → ieD6cW52 → gZWIQDA4 → cPJ7bQK8 → VT74ecGF → aVGCWTEA → QKHCWSPK → KB64edYQ → aXN5dMCA → YQL0iOJC → iM72gcN2 → geV0iE54 → icZGSA72 → gVPBXKE4 → cMH4eSN8 → aUB0iYFA → iQNEUMJ2 → gG70icT4 → icVCWE72 → gVKGSPE4 → cHC4eXS8 → aULAYOFA → QOF2gULK → eF62gdU6 → eYXEUCB6 → YNLFTOMC → ME30igVO → idH1hS62 → hfXAYC43 → ebOKOL86 → YT42gfGC → ebMCWN86 → YTK0iPGC → iMD4eWN2 → gaJ0iQ94 → icR6cI72 → gWV8aED4 → cSJGSQH8 → UCB6cYXG → WNLDVOME → JH30igSR → idB7bY62 → gXUMMFC4 → cLEjjUO8 → bVH5dSE9 → YSHAYSHC → OMBAYYNM → ON20ihMM → if20ih42 → igfa8432 → gdbRH864 → cXT9ZGC8 → UQLCWOJG → KE72gcVQ → eVH5dSE6 → ZXHAYSCB → PNLAYOML → O430igfM → idb1h862 → hfXSGC43 → ebLBXO86 → YTM2gNGC → eMD0iWN6 → iYJ0iQB2 → igN6cM32 → gdW0iD64 → icXIQC72 → gVL7bOE4 → cUH2gSF8 → eUFAYUF6 → YOFEUULC → MGF2gUTO → eFD1hWU6 → gYJEUQB4 → cNG6cTM8 → WUD0iWFE → iJIEURQ2 → gG96caT4 → cWRCWID8 → UKJ8aQPG → SE74ecVI → aVH9ZSEA → RPHAYSKJ → OB84ebYM → aTN1hMGA → gQD0iWJ4 → icJ6cQ72 → gWV6cED4 → cWJGSQD8 → UJC6cXQG → WLE6cVOE → WIH2gSRE → eIB8aYR6 → YSN8aMHC → SMB0iYNI → iNA0iZM2 → igP0iK32 → igd4e632 → gdaWC964 → cXRJPIC8 → UL95daOG → YRE2gVIC → eMH8aSN6 → YSB0iYHC → iNMAYNM2 → gO10iiL4 → ihc2g722 → gfeUE544 → cbZFTA88 → UTPDVKGG → IED4eWVS → aJH9ZSQA → RPB6cYKJ → WN84ebME → aTI0iRGA → iQD8aWJ2 → gSJ6cQH4 → cWB6cYD8 → WUNIQMFE → IF80ibUS → iTF9ZUG2 → gQFCWUJ4 → cKF6cUP8 → WUF4eUFE → aIFEUURA → QGF8aUTK → SFD5dWUI → YJF9ZUQC → QMF6cUNK → WF60idUE → iXIEURC2 → gLG8aTO4 → cSD2gWH8 → eUJAYQF6 → YOF6cULC → WMF2gUNE → eIF0iUR6 → iYF8aUB2 → gSNEUMH4 → cGB0iYT8 → iUNCWMF2 → gKF0iUP4 → icF4eU72 → gaVEUE94 → cRHFTSI8 → UEB8aYVG
947 max stepsC00000LMN → NMLBjXONN → YC1jjjhXC → iXX9jZCC2 → hZNKjOMA3 → gXF1jhUC4 → idUHjRF62 → hcOCjWL73 → gaQAjYJ94 → fXQEjUJC5 → eTJAjYQG6 → dUI9jZRF7 → cUKBjXPF8 → bRI9jZRI9 → aSH8jaSHA → bQJAjYQJ9 → aRF6jcUIA → dSLBjXOH7 → cSG6jcTH8 → dUMBjXNF7 → cSI7jbRH8 → cUK9jZPF8 → bTK9jZPG9 → aSJ8jaQHA → bQJ8jaQJ9 → bSH6jcSH9 → dTKAjYPG7 → cTI8jaRG8 → bUKAjYPF9 → aRJ9jZQIA → aQH7jbSJA → cRJ8jaQI8 → bUI7jbRF9 → cSMBjXNH8 → bRG5jdTI9 → eULAjYOF6 → dUJ8jaQF7 → cVLAjYOE8 → bSK9jZPH9 → aSI7jbRHA → cRJ9jZQI8 → bTH7jbSG9 → cSLBjXOH8 → bRG6jcTI9 → dTLAjYOG7 → cTI7jbRG8 → cULAjYOF8 → bSJ8jaQH9