Base 65: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0Γ → Β1 → z3
333 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 → WΓW
44 max stepsX000 → WΓΓW → WVWX → 1ΓΓΒ → Β0Β2
527 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 → iMΓfL
640 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 → vD1Αp8
739 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 → mXFΓmVH
889 max stepsG0000qyy → yyqFmC45 → uteWVO99 → lkG0ΒmII → ΒWTRaZW2 → z95ΓΓwt4 → yxq2zC55 → xtsdOA96 → rkiEnKIC → fZSNeaTO → IG85wuml → rmWSZWGC → fW6ΓΓvWO → weP8tdO7 → plGDomHE → caWTYWSR → B84ΓΓxus → yum1ΑG85 → ztmVWG94 → vkW0ΒWI8 → ΒnRΓΓaF2 → ΑnaCpSF3 → xdY7uUP6 → rnE3yoFC → vfaXUSN8 → nI82zukG → xmXRaVG6 → rW91ΑtWC → zkeΓΓNI4 → ykc5wQI5 → trSBqaBA → jgf7uNMK → nPKHkidG → XTODoeZW → bG60ΒwmS → ΒqW8tWC2 → zldΓΓOH4 → ylb7uRH5 → tnU9sYFA → kiY3yUKJ → vRO3yeb8 → vnG9smF8 → njYVWUJG → XQ40ΒycW → ΒuC0Βq82 → ΒzmdOG32 → zwWEnW64 → vqYΓΓTC8 → uqSHkaC9 → leT7uZOI → nTG5wmZG → rXW5wWVC → rf1ΓΓΑNC → ΒqdBqPC2 → zfeDoON4 → vbIFmkR8 → nXS9saVG → jX81ΑuVK → zmP1ΑdG4 → zvWDoW74 → voaΓΓRE8 → uoUDoYE9 → lba3ySRI → vTA7usZ8 → omi5wKGF → rZWNeWTC → fH5ΓΓwlO → xlY5wUH6 → sqU3yYCB → vhe3yOL8 → vnMFmgF8 → nYXJiVUG → XP41ΑydW → zuE0Βo84 → ΒvmZSG72 → zoW6vWE4 → vpZΓΓSD8 → upTFmZD9 → lcX5wVQI → rTC1ΑqZC → zfe5wON4 → vrIFmkB8 → ngXRaVMG → XK91ΑtiW → zkO0ΒeI4 → ΒvSFma72 → zoX7uVE4 → vna1ΑSF8 → znY7uUF4 → vnY3yUF8