Base 64: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps1 → 0 → 0
28 max steps20 → 1Α → y3 → u7 → mF → WV → 0Β → Α1 → y3
334 max steps100 → 0ΒΒ → ΑΒ1 → zΒ2 → yΒ3 → xΒ4 → wΒ5 → vΒ6 → uΒ7 → tΒ8 → sΒ9 → rΒA → qΒB → pΒC → oΒD → nΒE → mΒF → lΒG → kΒH → jΒI → iΒJ → hΒK → gΒL → fΒM → eΒN → dΒO → cΒP → bΒQ → aΒR → ZΒS → YΒT → XΒU → WΒV → VΒW → VΒW
416 max steps1004 → 40Αy → Αt72 → ylF4 → uVV8 → lΒΒG → lFlH → WTXW → 3ΒΒy → y2y4 → wt76 → qlFC → eVVO → FΒΒm → mEmG → YVVU → 3ΒΒy
530 max steps10009 → 90ΒΑt → ΒqΒA1 → ΑqΒA2 → zpΒB3 → ynΒD4 → xkΒG5 → wgΒK6 → vbΒP7 → uVΒV8 → tOΒc9 → sUΒWA → rNΒdB → qTΒXC → pMΒeD → oSΒYE → nLΒfF → mRΒZG → lKΒgH → kQΒaI → jJΒhJ → iPΒbK → hIΒiL → jMΒeJ → iMΒeK → hLΒfL → gLΒfM → gJΒhM → iKΒgK → hNΒdL → gJΒhM
669 max steps100037 → 730Αyv → ΑvnD62 → ypZRC4 → ud7tO8 → nlEmGF → ZXUWUT → 631zyw → yvpB64 → updNC8 → mdFlOG → XVEmWV → Y20ΑzU → Αx3x42 → yus874 → unjHE8 → mZRZSG → W86utW → okΒΒGE → nl3xGF → uYUWT8 → m51zwG → yrVVA4 → ugΒΒK8 → thDnK9 → kaMeRI → SI8sja → kR7taI → mS8sZG → kW6uVI → oS0ΑZE → Αa6uR2 → yo8sD4 → ukaQH8 → mT9rYG → iW4wVK → sO0ΑdA → ΑiEmJ2 → yYOcT4 → uE4wn8 → smYSFA → iX5vUK → qO2ydC → weEmN6 → qYGkTC → eU4wXO → sG2ylA → wiUWJ6 → qP1zcC → yeCoN4 → ucGkP8 → mUCoXG → cW2yVQ → wC0Αp6 → ΑqcOB2 → yfDnM4 → uaIiR8 → mQ8sbG → kWAqVI → gS0ΑZM → ΑK6uh2 → yoMeD4 → ubHjQ8 → mSAqZG → gW6uVM → oK0ΑhE → ΑaMeR2 → yI8sj4 → ukQaH8 → mT9rYG
745 max steps1000000 → 0ΒΒΒΒΒΒ → ΑΒΒΒΒΒ1 → Α0ΒΒΒΑ2 → Βz0ΒΑ21 → ΒΑxΒ311 → ΑΑwΒ412 → ΑyvΒ532 → zxsΒ843 → yvoΒC64 → xsiΒI95 → woZΒRD6 → vjMΒeI7 → udMΒeO8 → tYFΒlT9 → seHΒjNA → rbLΒfQB → qWEΒmVC → pcGΒkPD → oZKΒgSE → nUDΒnXF → oYIΒiTE → nWEΒmVF → nYGΒkTF → mXGΒkUG → lWFΒlVH → mUFΒlXG → mWGΒkVG → lWEΒmVH → nVFΒlWF → mYFΒlTG → mWHΒjVG → lVDΒnWH → oWFΒlVE → nZFΒlSF → mYIΒiTG → lUEΒmXH → nVGΒkWF → mXEΒmUG → nWHΒjVF → mWDΒnVG → oXGΒkUE → nYFΒlTF → mYHΒjTG → lVFΒlWH → mUFΒlXG
8106 max stepsV0000000 → UΒΒΒΒΒΒX → XTΒΒΒΒXV → YWUTXXVU → 5330Αyyx → Αvvr9662 → ypphJCC4 → uddNdOO8 → mGFEmmlG → YXWUWVUU → 4320Αzyy → Αxvt7642 → ytplFC84 → uldVVOG8 → mVEΒΒmWG → nlHFlkGF → YWVSYWVU → 6410ΑΑxw → ΑztpB822 → yxldNG44 → utVFlW88 → mlW0ΑVGG → ΑWV0ΑWV2 → Αy10ΑΑ32 → Αzyu6322 → yxvnD644 → utpZRC88 → mld7tOGG → mWVEmWVG → YW10ΑΑVU → Αz40Αx22 → Αyxs8432 → yvtjH864 → uplRZGC8 → mdV7tWOG → mWF0ΑmVG → ΑXW0ΑVU2 → Αy30Αy32 → Αyvu6632 → yvpnDC64 → updZROC8 → mdF7tmOG → mXWEmVUG → YW30ΑyVU → Αv40Αx62 → ΑytoC832 → yvlbPG64 → upVBpWC8 → med0ΑONG → ΑWHEmkV2 → yYT0ΑYT4 → Αu54ww72 → ysrmEA94 → ujhXTKI8 → mRN3xeaG → uWH8skV8 → mkT0ΑYHG → ΑWT4wYV2 → ys50Αw94 → ΑuriIA72 → ynhPbKE4 → uZNBpeS8 → meH6ukNG → oWTGkYVE → aU50ΑwXS → Αr82ytA2 → ywlgKG54 → urVLfWA8 → mhK0ΑhKG → ΑWNMeeV2 → yIH0Αkj4 → ΑuTQaY72 → ynA4wrE4 → ushYSK98 → mjN5veIG → qWRGkaVC → eU90ΑsXO → ΑjG2ylI2 → ywVQaW54 → urA0ΑrA8 → ΑmhgKKF2 → yXNLfeU4 → uKH2ykh8 → wmTMeYF6 → qXI4wjUC → seR2yaNA → wiH8skJ6 → qkTOcYHC → eTE4wnYO → sZG4wlSA → siV6uWJA → oiP0ΑcJE → ΑaPCocR2 → ycD8soP4 → ukbCoQH8 → mcTAqYPG → gWD4woVM → sbK0ΑhQA → ΑiNAqeJ2 → ygPGkcL4 → uULCogX8 → mcL2ygPG → wWLCogV6 → qcL0ΑgPC → ΑeLCogN2 → ycLGkgP4 → uULCogX8