Base 43: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
29 max steps10 → 0g → f1 → d3 → Z7RFBVJN3dZ7
324 max steps100 → 0gg → fg1 → eg2 → dg3 → cg4 → bg5 → ag6 → Zg7 → Yg8 → Xg9 → WgA → VgB → UgC → TgD → SgE → RgF → QgG → PgH → OgI → NgJ → MgK → LgLKgMLgL
411 max stepsM000 → LggL → LKLM → 1ggf → f0f2fc32dY74ZQF8RAVGLAVML0fMf0f2
522 max steps10000 → 0gggg → fggg1 → f0gf2 → gcg31 → fcg32 → ebg43 → dZg64 → cWg95 → bSgD6 → aNgI7 → ZHgO8 → YHgO9 → XGgPA → WGgPB → VFgQC → UFgQD → TEgRE → SEgRF → SCgTFUDgSDTGgPESCgTF
670 max steps7000bb → bb6Z56 → WVSDBB → LKERMM → D20feU → fcGP42 → dY8X84 → ZQOHG8 → RA6ZWG → TMAVKE → LF1eRM → dC0fU4 → fZHO72 → dS6ZE4 → ZTDSD8 → RGERQG → DB9WVU → NKGPMK → 931edY → daOH64 → ZU6ZC8 → TRHOFE → FC6ZUS → TICTOE → HF5aRQ → VC8XUC → PJHONI → 863caZ → ZUQFC8 → RIAVOG → LB5aVM → VK0fMC → fJ1eN2 → ec3c43 → bZX876 → VSOHEC → JE6ZSO → TE4bSE → XFDSRA → NFBURK → JC2dUO → bI4bO6 → XV5aBA → VNJMJC → J42dcO → bY4b86 → XVPGBA → NK8XMK → P31edI → da6Z64 → ZUSDC8 → RIEROG → DB5aVU → VKGPMC → J91eXO → dO4bI4 → ZX5a98 → VRNIFC → JC4bUO → XI4bOA → XN5aJA → VN3cJC → ZJ3cN8ZR3cF8ZRBUF8RJBUNGJB3cVOZK4bM8XR1eFAdNBUJ4ZJ3cN8
744 max steps1000001 → 10gggfg → gf0gf11 → gfdg211 → ffcg312 → fdbg432 → ecYg743 → daUgB64 → cXOgH95 → bTFgQD6 → aODgSI7 → ZN9gWJ8 → YQCgTG9 → XMCgTKA → WL8gXLB → YMAgVK9 → XOAgVIA → WNCgTJB → VK9gWMC → XKAgVMA → WNAgVJB → WLBgULB → VL8gXLC → YL9gWL9 → XPAgVHA → WNDgSJB → VJ8gXNC → YLBgUL9 → XN8gXJA → YNDgSJ9 → XL8gXLA → YNBgUJ9 → XNAgVJA → WNBgUJB → VLAgVLC → WJ9gWNB → XLCgTLAWL7gYLBZNAgVJ8YPBgUH9XNCgTJAWL9gWLBXLAgVLAWN9gWJBXLCgTLA
8115 max stepsG0000KWW → WWKFQMAB → MLB1eVLL → dK0ggfM4 → gcLGPL41 → fY8ggX82 → eYX0f983 → fbQNIG52 → dWA4bWA4 → ZXMLKK98 → RO20feIG → fcB5aV42 → dYVJMB84 → ZQK2dMG8 → bRA1eWF6 → dVMBUKB4 → ZKJ1eNM8 → dR41ecF4 → dZYBU874 → ZSQINGE8 → REA4bWSG → XMEAVSKA → NLE1eSLK → dE2ggdS4 → ecPAVH43 → bYL7YL86 → VRPggGFC → URF1eRFD → dHCBUUP4 → ZJI7YON8 → SQ63caGF → ZUD9WTC8 → RNIFQOJG → CA63caWV → ZUMINKC8 → RI51ebOG → dWB5aVA4 → ZVMJMKB8 → RK31edMG → daB1eV64 → dZUJMC74 → ZSI2dOE8 → bRE5aSF6 → WUEBUSCB → LJIDSONM → F640fcaS → fYUCTC82 → dQIGPOG4 → ZA95aXW8 → VROLKIFC → JC60faUO → fUI4bOC2 → dXI5aO94 → ZVO5aIB8 → VRK5aMFC → VJC1eUNC → dJI3cON4 → aY63ca87 → ZUTPGDC8 → RIG8XQOG → PBA5aWVI → VMK6ZMKC → TJ21eeNE → dcF3cR44 → aYYBU887 → TQQINGGE → FAA4bWWS → XMMCTKKA → NH21eePK → dc82dY44 → bZYPG876 → VSQ8XGEC → PJE9WSNI → NE73cZSK → ZSE2dSE8 → bREDSSF6 → VFEBUSRC → KIEBUSON → JE62daSO → bUE4bSC6 → XVIDSOBA → NKF5aRMK → VC31edUC → daJHON64 → ZU73cZC8 → ZSRHOFE8 → REC6ZUSG → TIEAVSOE → LFE5aSRM → VEC0fUSC → fJIDSON2 → dF63caR4 → aYUBUC87 → TQJHONGE → FA73cZWS → ZSMCTKE8 → RHE1eSPG → dEB7YVS4 → ZRKDSMF8 → RFC1eURG → dICAVUO4 → ZLI5aOL8 → VR5ggaFC → bUL3cLC6 → ZVHggOB8 → YVI6ZOB9 → TPK5aMHE → VF81eYRC → dQJBUNG4 → ZJA3cWN8 → ZRM3cKF8 → ZRC1eUF8 → dRIBUOF4 → ZJC5aUN8VRI3cOFCZJC5aUN8
948 max stepsB000000Lg → gLAgggVL1 → fWLKgLLA2 → eVBgggUB3 → dVV9gWBB4 → cULJgMLC5 → bQB0gfVG6 → gZQEgRG71 → fZLAgVL72 → eYP9gWH83 → dWPEgRHA4 → cTI9gWOD5 → bTJAgVND6 → aRI9gWOF7 → ZRH8gXPF8 → YRI9gWOF9 → XPH8gXPHA → YNG7gYQJ9 → ZPI6gZOH8 → aRI6gZOF7 → aTK8gXMD7 → ZSK8gXME8 → YRJ7gYNF9 → ZPJ7gYNH8 → ZRH5gaPF8 → bSK9gWME6 → aSI7gYOE7 → ZTK9gWMD8 → YQJ8gXNG9 → YPH6gZPH9 → aQH7gYPG7 → ZTI8gXOD8YRKAgVMF9XOG6gZQIAaPH7gYPH7ZTH7gYPD8ZRLBgULF8YOF5gaRI9bRJ8gXNF6aTI7gYOD7ZTLAgVLD8YPI7gYOH9ZPH6gZPH8aRI7gYOF7ZTJ8gXND8YRK9gWMF9XPH6gZPHAaPG7gYQH7ZTI8gXOD8