Base 65: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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
28 max steps10 → 0Γ → Β1 → z3v7nFXVz3
335 max steps100 → 0ΓΓ → ΒΓ1 → ΑΓ2 → zΓ3 → yΓ4 → xΓ5 → wΓ6 → vΓ7 → uΓ8 → tΓ9 → sΓA → rΓB → qΓC → pΓD → oΓE → nΓF → mΓG → lΓH → kΓI → jΓJ → iΓK → hΓL → gΓM → fΓN → eΓO → dΓP → cΓQ → bΓR → aΓS → ZΓT → YΓU → XΓV → WΓWVΓXWΓW
410 max stepsX000 → WΓΓW → WVWX → 1ΓΓΒ → Β0Β2Βy32zu74vmF8nWVGX0ΒWΒ0Β2
531 max stepsV0000 → UΓΓΓY → YTΓYV → Z2ΓzU → ΑUΓX3 → zVΓW4 → yTΓY5 → xUΓX6 → wSΓZ7 → vTΓY8 → uRΓa9 → tSΓZA → sQΓbB → rRΓaC → qPΓcD → pQΓbE → oOΓdF → nPΓcG → mNΓeH → lOΓdI → kMΓfJ → jNΓeK → iLΓgL → hMΓfM → gKΓhN → iJΓiL → jMΓfK → iMΓfLhLΓgMhKΓhMiKΓhLiMΓfL
661 max steps1000FW → WF0ΒnX → ΒY0ΒU2 → Βz3y32 → zwu764 → vqmFC8 → neWVOG → XG0ΒmW → ΒW0ΒW2 → ΒyΓΓ32 → Αz2z33 → ywv665 → tqoDCA → jeaROK → PG8tme → lWEnWI → ZSΓΓZU → aXΓΓUT → ZY2zUU → x53yx6 → vsqBA8 → nieNKG → XOGleW → VG0ΒmY → ΒW2zW2 → zwΓΓ54 → yx2z55 → xtrA96 → rkgLIC → fSKhaO → NH7ulg → nUIjYG → XR3ybW → vA0Βs8 → ΒnhKF2 → zYMfU4 → vJ3yj8 → vnPcF8 → nYCpUG → dX3yVQ → vD1Αp8znbQF4vYArU8nh3yLGvXLgV8nL1ΑhGzXLgV4vL1Αh8znLgF4vYKhU8nN3yfGvXHkV8nT1ΑZGzX5wV4vr1ΑB8znfMF4vYIjU8nR3ybGvX9sV8nj1ΑJGzXPcV4vD1Αp8
741 max steps80000VW → WV7ΓuXX → vP0ΓΒd8 → ΓtVΓW91 → ΒtNΓe92 → ΑsVΓWA3 → zqMΓfC4 → ynTΓYF5 → xjJΓiJ6 → wePΓcO7 → vYEΓnU8 → uhIΓjL9 → tcNΓeQA → sWDΓoWB → rfHΓkNC → qaMΓfSD → pUCΓpYE → qbKΓhRD → pWFΓmWE → oaFΓmSF → nZJΓiTG → mUEΓnYH → oWHΓkWF → nXDΓoVG → pYHΓkUE → oYFΓmUF → nZHΓkTG → mWGΓlWH → mVEΓnXH → oWGΓlWF → nYEΓnUG → oXIΓjVF → nWDΓoWG → pYGΓlUE → oZGΓlTF → nYHΓkUG → mWFΓmWH → nVFΓmXG → nXGΓlVG → mXFΓmVHnVGΓlXGmXFΓmVH
892 max stepsG0000Uoo → ooUFmYEF → aZX3yVTT → v761Αwv8 → zqomFEC4 → veaWVSO8 → nG80ΒumG → ΒmXVWVG2 → zW20ΒΑW4 → ΒyuΓΓ742 → Αyu3y843 → xvulG876 → romUXGEC → faW2zWSO → xH7ΓΓul6 → wvg8tM77 → polJiHEE → baUOdYSS → F983yuto → vmkYTIG8 → nWS4xaWG → tX7ΓΓuVA → vsPLgdA8 → niLDohKG → bXOLgeVS → LG91Αtmi → zkWMfWI4 → vSIΓΓja8 → ukT8tZI9 → mkS5waIH → rVS7uaXC → nf81ΑuNG → zmXHkVG4 → vWT1ΑZW8 → zn5ΓΓwF4 → yxk8tI55 → tslRaHAA → jiU8tYKK → lPO3yedI → vTGDomZ8 → nbW5wWRG → rX9ΓΓsVC → tqNJifCA → jePHkdOK → TPGDomda → bWE6voWS → pa8ΓΓtSE → uoREnbE9 → laZ9sTSI → jT85wuZK → rmP5wdGC → rfWDoWNC → fbHΓΓkRO → leJ3yjOI → vTQFmcZ8 → nXC5wqVG → reX1ΑVOC → zfG1ΑmN4 → zvWHkW74 → voSΓΓZE8 → uoTEnZE9 → laZ5wTSI → rT85wuZC → rmf5wNGC → rfWHkWNC → fTHΓΓkZO → leH5wlOI → rUTFmZYC → fX63ywVO → vqH1ΑlC8 → zneTYOF4 → vYG4xmU8 → tnW3yWFA → vjXΓΓUJ8ujRBqbJ9lfQ9scNIjTIBqkZKfSP5wdaOrHE7uolCnfaTYSNGXI84xukWtmS0ΒaGAΒjW7uWJ2znPΓΓcF4ynaArSF5thY7uULAnjM3ygJGvXQJicV8nPC1ΑqdGzeXDoVO4vbG1ΑmR8znW9sWF4vjXΓΓUJ8