Base 75: 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 steps1 → 0 → 0
213 max steps10 → 0Ν → Μ1 → Κ3 → Ζ7 → xF → hV → BΒ → pN → Rl → Jt → Zd → 3Κ → Ζ7
340 max steps100 → 0ΝΝ → ΜΝ1 → ΛΝ2 → ΚΝ3 → ΙΝ4 → ΘΝ5 → ΗΝ6 → ΖΝ7 → ΕΝ8 → ΔΝ9 → ΓΝA → ΒΝB → ΑΝC → zΝD → yΝE → xΝF → wΝG → vΝH → uΝI → tΝJ → sΝK → rΝL → qΝM → pΝN → oΝO → nΝP → mΝQ → lΝR → kΝS → jΝT → iΝU → hΝV → gΝW → fΝX → eΝY → dΝZ → cΝa → bΝb → aΝc → bΝb
424 max stepsc000 → bΝΝb → babc → 1ΝΝΜ → Μ0Μ2 → ΜΙ32 → ΚΕ74 → ΖwF8 → xgVG → hAΒW → rAΒM → rUhM → VCzi → nCzQ → nMpQ → TMpk → TGvk → fGvY → f6ΖY → z6ΖE → zkRE → lItS → bItc → b0Μc → Μ0Μ2
535 max steps10000 → 0ΝΝΝΝ → ΜΝΝΝ1 → Μ0ΝΜ2 → ΝΙΝ31 → ΜΙΝ32 → ΛΘΝ43 → ΚΖΝ64 → ΙΓΝ95 → ΘyΝD6 → ΗtΝI7 → ΖnΝO8 → ΕgΝV9 → ΔYΝdA → ΓUΝhB → ΒXΝeC → ΑTΝiD → zWΝfE → ySΝjF → xVΝgG → wRΝkH → vUΝhI → uQΝlJ → tTΝiK → sPΝmL → rSΝjM → qOΝnN → pRΝkO → oNΝoP → pOΝnO → oQΝlP → nNΝoQ → pNΝoO → pQΝlO → oOΝnP → oOΝnP
6253 max stepsc00000 → bΝΝΝΝb → baΝΝbc → cb0Μbb → Μ0ΝΝΜ2 → ΝΚΝΝ21 → ΜΛ2Κ22 → ΚΙΗ544 → ΖΕΑB88 → xwoNGG → hgQlWW → LB9ΓΒs → tqWfMK → ZU8Δie → vE4ΘyI → ΔkcZSA → tI2ΚuK → ΘcYda6 → Β51ΛΘC → ΚΓoNA4 → ΖsQlK8 → xYKreG → hX5ΗfW → ΒB7ΕΒC → xqoNMG → hUQliW → LEAΒys → rkWfSM → VI8Δui → vcCzaI → nd1ΛZQ → ΚN3Ιp4 → ΗΕRk87 → zwItGE → lgabWS → JA0ΜΓu → ΜsabK2 → ΚY0Μe4 → ΜΖ5Η72 → ΚΒxEB4 → ΖqiTM8 → xUExiG → jhDyVU → lFBΑxS → piItUO → bRDylc → lK0ΜsS → ΜYIte2 → Κb5Ηb4 → ΖΑΝΝB8 → ΕΒ4ΘB9 → ΔvpMHA → teSjYK → ZH5Ηve → Βe4ΘYC → Δp5ΗNA → ΒtRkJC → paItcO → bR1Λlc → ΚK0Μs4 → ΜΖXe72 → Κy6ΖE4 → ΖzjSD8 → xmGvQG → hfLqXW → VB7ΕΒi → xqCzMG → nhTiVQ → NFBΑxq → piSjUO → RHDyvm → leKrYS → XJ5Ηtg → Βa8ΔcC → vp1ΛNI → ΚdRkZ4 → ΖJ3Ιt8 → ΖxZcF8 → xi2ΚUG → ΘhDyV6 → ΒlBΑRC → qoJsON → ZTPmje → NG4Θwq → ΔgSjWA → tH9ΓvK → teYdYK → Z64ΘΗe → ΔΑ4ΘCA → ΔtnOJA → taOncK → ZP1Λne → ΚO4Θo4 → ΖΔPm98 → xuMpIG → hcSjaW → HB1ΛΒw → ΚqeXM4 → ΖU6Ζi8 → zxDyFE → mkhUSR → LICzus → ncWfaQ → N91ΛΔq → ΚuSjI4 → ΖcGva8 → xf1ΛXG → Κh7ΕV4 → ΖxBΑF8 → xphUNG → hSCzkW → nIAΒuQ → rcMpaM → VT1Λji → ΚGCzw4 → ΖnfWP8 → xO8ΔoG → vhPmVI → dNBΑpa → pS2ΚkO → ΘRHul6 → ΒdJsZC → pZ3ΙdO → ΖR3Ιl8 → ΖxJsF8 → xiYdUG → hE4ΘyW → ΔkAΒSA → trHuLK → dZVgda → B42ΚΙΓ → ΘΕqL86 → ΒwUhGC → pgCzWO → nR9ΓlQ → tNJspK → aYRked → J62ΚΗu → ΘΑabC6 → Βo0ΜOC → ΜpPmN2 → ΚSMpk4 → ΖTHuj8 → xdFwZG → ig3ΙWV → ΖD9Γz8 → xtlQJG → haKrcW → XB1ΛΒg → Κq8ΔM4 → ΖvTiH8 → xeExYG → jh5ΗVU → ΒFBΑxC → qohUON → TQCzmk → nMGvqQ → fUMpiY → TE6Ζyk → zkGvSE → lfHuXS → dJ7Εta → xa2ΚcG → Θh1ΛV6 → ΚΒBΑB4 → ΖqoNM8 → xUQliG → hLDyrW → lWAΒgS → rJ9ΓtM → taUhcK → ZD1Λze → Κm4ΘQ4 → ΖΔLq98 → xuUhIG → hcCzaW → nB1ΛΒQ → ΚqMpM4 → ΖUSji8 → xHDyvG → lhdYVS → JC4ΘΑu → ΔoabOA → tQ0ΜmK → ΜZLqd2 → ΚV3Ιh4 → ΗΕBΑ87 → zwoNGE → lgQlWS → LJ9Γts → taWfcK → Z91ΛΔe → Κu4ΘI4 → ΖΔba98 → xu0ΜIG → ΜhbaV2 → ΚC0ΜΑ4 → ΜΖnO72 → ΚyOnE4 → ΖkOnS8 → xPHunG → hdNoZW → RB3ΙΒm → ΖqKrM8 → xXTifG → hF7ΕxW → xiAΒUG → rhDyVM → lVBΑhS → pJBΑtO → paQlcO → RL1Λrm → ΚWKrg4 → ΖX9Γf8 → xt7ΕJG → xhZcVG → hC2ΚΑW → ΘoAΒO6 → ΒrPmLC → pWMpgO → TR9Γlk → tKGvsK → fZXedY → 863ΙΗΖ → ΖΑwFC8 → xogVOG → hQAΒmW → rMAΒqM → rVTihM → VFBΑxi → piCzUO → nRDylQ → lNJspS → ZSItke → bI4Θuc → Δc0ΜaA → Μt1ΛJ2 → ΛΙZc43 → ΘΕ2Κ86 → ΘΒvGB6 → ΒqeXMC → pU6ΖiO → zRDylE → mkJsSR → ZLHure → dW4Θga → ΔA2ΚΓA → ΘtrKJ6 → ΒaWfcC → p91ΛΔO → ΚuQlI4 → ΖcKra8 → xX1ΛfG → Κh7ΕV4
751 max stepsS00000b → bRΝΝΝkc → lbZΝcbS → kC0ΝΜΑT → ΝzWΝfD1 → ΜzSΝjD2 → ΛyWΝfE3 → ΚwRΝkG4 → ΙtUΝhJ5 → ΘpOΝnN6 → ΗkQΝlS7 → ΖgIΝtW8 → ΕnMΝpP9 → ΔiPΝmUA → ΓeHΝuYB → ΒlLΝqRC → ΑgOΝnWD → zcGΝvaE → yjKΝrTF → xeNΝoYG → waFΝwcH → xfLΝqXG → wcIΝtaH → veIΝtYI → udKΝrZJ → taHΝucK → vaIΝtcI → udIΝtZJ → ubJΝsbJ → tbGΝvbK → wbHΝubH → vfIΝtXI → udLΝqZJ → tZGΝvdK → wbJΝsbH → vdGΝvZI → wdLΝqZH → vbGΝvbI → wdJΝsZH → vdIΝtZI → udJΝsZJ → tbIΝtbK → uZHΝudJ → vbKΝrbI → ubFΝwbJ → xdIΝtZG → wfJΝsXH → vdKΝrZI → ubHΝubJ → vbIΝtbI → udHΝuZJ → vbKΝrbI