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 steps100
213 max steps10 → 0Ν → Μ1 → Κ3 → Ζ7xFhVpNRlJtZdΖ7
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 → bΝbaΝcbΝb
424 max stepsc000 → bΝΝb → babc → 1ΝΝΜ → Μ0Μ2ΜΙ32ΚΕ74ΖwF8xgVGhAΒWrAΒMrUhMVCzinCzQnMpQTMpkTGvkfGvYf6ΖYz6ΖEzkRElItSbItcb0ΜcΜ0Μ2
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 → oOΝnPoOΝnP
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 → Κh7ΕV4ΖxBΑF8xphUNGhSCzkWnIAΒuQrcMpaMVT1ΛjiΚGCzw4ΖnfWP8xO8ΔoGvhPmVIdNBΑpapS2ΚkOΘRHul6ΒdJsZCpZ3ΙdOΖR3Ιl8ΖxJsF8xiYdUGhE4ΘyWΔkAΒSAtrHuLKdZVgdaB42ΚΙΓΘΕqL86ΒwUhGCpgCzWOnR9ΓlQtNJspKaYRkedJ62ΚΗuΘΑabC6Βo0ΜOCΜpPmN2ΚSMpk4ΖTHuj8xdFwZGig3ΙWVΖD9Γz8xtlQJGhaKrcWXB1ΛΒgΚq8ΔM4ΖvTiH8xeExYGjh5ΗVUΒFBΑxCqohUONTQCzmknMGvqQfUMpiYTE6ΖykzkGvSElfHuXSdJ7Εtaxa2ΚcGΘh1ΛV6ΚΒBΑB4ΖqoNM8xUQliGhLDyrWlWAΒgSrJ9ΓtMtaUhcKZD1ΛzeΚm4ΘQ4ΖΔLq98xuUhIGhcCzaWnB1ΛΒQΚqMpM4ΖUSji8xHDyvGlhdYVSJC4ΘΑuΔoabOAtQ0ΜmKΜZLqd2ΚV3Ιh4ΗΕBΑ87zwoNGElgQlWSLJ9ΓtstaWfcKZ91ΛΔeΚu4ΘI4ΖΔba98xu0ΜIGΜhbaV2ΚC0ΜΑ4ΜΖnO72ΚyOnE4ΖkOnS8xPHunGhdNoZWRB3ΙΒmΖqKrM8xXTifGhF7ΕxWxiAΒUGrhDyVMlVBΑhSpJBΑtOpaQlcORL1ΛrmΚWKrg4ΖX9Γf8xt7ΕJGxhZcVGhC2ΚΑWΘoAΒO6ΒrPmLCpWMpgOTR9ΓlktKGvsKfZXedY863ΙΗΖΖΑwFC8xogVOGhQAΒmWrMAΒqMrVTihMVFBΑxipiCzUOnRDylQlNJspSZSItkebI4ΘucΔc0ΜaAΜt1ΛJ2ΛΙZc43ΘΕ2Κ86ΘΒvGB6ΒqeXMCpU6ΖiOzRDylEmkJsSRZLHuredW4ΘgaΔA2ΚΓAΘtrKJ6ΒaWfcCp91ΛΔOΚuQlI4ΖcKra8xX1ΛfGΚh7ΕV4
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 → vbKΝrbIubFΝwbJxdIΝtZGwfJΝsXHvdKΝrZIubHΝubJvbIΝtbIudHΝuZJvbKΝrbI