Base 27: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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
27 max steps10 → 0Q → P1 → N3 → J7BF3NJ7
316 max steps100 → 0QQ → PQ1 → OQ2 → NQ3 → MQ4 → LQ5 → KQ6 → JQ7 → IQ8 → HQ9 → GQA → FQB → EQC → DQDCQEDQD
413 max stepsE000 → DQQD → DCDE → 1QQP → P0P2PM32NI74JAF8B4LGH4LAH6JAD6JED0PEP0P2
519 max steps10000 → 0QQQQ → PQQQ1 → P0QP2 → QMQ31 → PMQ32 → OLQ43 → NJQ64 → MGQ95 → LCQD6 → K8QH7 → JBQE8 → I7QI9 → J8QH8 → IAQF9 → H7QIA → J7QI8 → JAQF8 → I8QH9I8QH9
674 max steps300000 → 2QQQQO → O1QQO3 → PMQQ32 → ON2N33 → MKJ665 → HECDCA → 720POK → PMCD42 → NI0P84 → PJ9G72 → NC6JE4 → JD1OD8 → NAQQF4 → MG7IA5 → HB5KFA → F73MJCJC2NE8LB1OF6NF3MB4KI3M87JD9GD8B6QQJGKF2NB7LD3MD6JEQQB8IF4LB9H93MHAJ86JI8DB9GFE740PMKPICD82NA0PG4PJ5K72NFBEB4J42NM8LIAF86FA4LGCH62NKALE6JC6FD1ODCN2QQN4OLQQ43NM2N44LJH876FC8HEC931ONINK8H64JE8HC8B91OHGN84LI4JH9G98B86JIGDA4LGEH60PKAPE6JC2ND1OD4NIQQ74MJ4L75IGBEA9962NKILE8HC6F91OHCN82NI4LJ9G76FC6JECD31ONENK0P64PJDC72NC0PE4PJ1O72OMBE43LI2N86LF9GB6F73MJC
738 max steps700000C → C6QQQJF → KEAQFC7 → JA2QNG8 → OF8QHB3 → NG5QKA4 → MI9QG85 → LE8QHC6 → KD4QLD7 → ME6QJC5 → LG6QJA6 → KF8QHB7 → JC5QKE8 → LC6QJE6 → KF6QJB7 → KD7QID7 → JD4QLD8 → MD5QKD5 → LH6QJ96 → KF9QGB7 → JB4QLF8 → MD7QID5 → LF4QLB6 → MF9QGB5 → LD4QLD6 → MF7QIB5 → LF6QJB6 → KF7QIB7 → JD6QJD8 → KB5QKF7 → LD8QHD6KD3QMD7NF6QJB4MH7QI95LF8QHB6KD5QKD7LD6QJD6KF5QKB7LD8QHD6
867 max steps60000DQQ → QQD5KD01 → QPEQQB11 → PPFAFB12 → ON53ML33 → LKJFA766 → FEC4LECC → H321OONA → NMK6J644 → JIECDC88 → BA20POGG → PM64LK42 → NIHDC984 → JA80PIG8 → PBA5KGF2 → NF63MKB4 → KIE3MC87 → JDA1OGD8 → NB5QQKF4 → MLC4LE55 → IGG1OAA9 → N965KKH4 → JFE7ICB8 → CA41OMGF → NI62NK84 → LJE9GC76 → FC71OJEC → NC31ONE4 → NKJ1O764 → NJEBEC74 → JC31ONE8 → NKB1OF64 → NJE3MC74 → KIC1OE87 → NDA1OGD4 → NJ5QQK74 → MLG0PA55 → PHG5KA92 → NF85KIB4 → JFA3MGB8 → JB63MKF8 → JEB3MFC8 → JB41OMF8NIB3MF84KIA3MG87JDA5KGD8FB5QQKFCLF7QQIB6KJA2NG77LDC5KED6GE1QQOCBPFC1OEB2OM41OM43NLIH8854JGA8HGA8B965KKHGFE84LICCHA31ONGANK75KJ64JFEBECB8B431ONMGNKI4L864JHE9GC98B871OJIGNCA4LGE4JH61OK98NEB7IFC4JB41OMF8
943 max stepsD00000DIO → OIDCQDD83 → NG5QQQKA4 → MLG6QJA55 → LHF8QHB96 → KD85QKID7 → LDC4QLED6 → MF90QPHB5 → QKD5QKD61 → PLE6QJC52 → OKF6QJB63 → NIE7QIC84 → MGA5QKGA5 → LHA5QKG96 → LFB6QJFB6 → KF83QMIB7 → NFC6QJEB4 → MH82QNI95 → OIE8QHC83 → NGA4QLGA4 → MJB5QKF75 → LHD7QID96 → KE93QMHC7 → NFB4QLFB4 → MJA3QMG75 → NHF8QHB94 → MF85QKIB5 → LHC6QJE96 → KFA4QLGB7 → MEA4QLGC5 → MHB3QMF95 → NHD5QKD94 → MIB3QMF85 → NHE6QJC94 → MHA4QLG95 → MHC6QJE95LGA4QLGA6MFB5QKFB5LH93QMH96NGC7QIEA4MG83QMIA5NHE7QIC94MG94QLHA5MHC6QJE95
1089 max steps1000002DDD → DDD20PODDE → PM0QQQQP42 → QOM3QQM421 → PONJQQ6322 → OOMI3M8423 → MLJI9G8755 → HGCA6JGEAA → D7661OKKJE → NEEC0PECC4 → PJ221OOO72 → OMMMBE4443 → LIII2N8886 → LFAA9GGGB6 → F7663MKKJC → JEEC2NECC8 → LB221OOOF6 → NMMF3MB444 → KIII3M8887 → JDAA9GGGD8 → B765QQKKJG → LKD92NHD66 → LFE7QQICB6 → KJA60PKG77 → PEDC5KEDC2 → NF21QQOOB4 → POKD7ID622 → NMEAQQFC44 → MMDA0PGD45 → PIH5QQK982 → OLHB0PF953 → PLG83MIA52 → NJGA5KGA74 → JFC65KKEB8 → FEB41OMFCC → NI431ONM84 → NKJI9G8764 → JECA6JGEC8 → DB621OOKFE → NME40PMC44 → PJII1O8872 → OMCA9GGE43 → LI761OKJ86 → NFEC9GECB4 → J7421OOMJ8 → NMICAFE844 → JIA51OLG88 → NGBA5KGFA4 → JF663MKKB8 → JEEB3MFCC8 → JB421OOMF8 → NMIB3MF844 → KIIA3MG887 → JDAA5KGGD8 → FB65QQKKFC → LK97QQIH66 → KKEB0PFC67 → PED41OMDC2 → OMI1QQO843 → PNKG3MA632 → NKJE5KC764 → JFEC1OECB8 → NB421OOMF4 → NMJI3M8744 → KIIC9GE887 → DAA71OJGGE → NC660PKKE4 → PJEE1OCC72 → OMC21OOE43 → NMLI1O8544 → NJIG9GA874 → JCA75KJGE8 → FCB61OKFEC → NE431ONMC4 → NKJI1O8764 → NJEC9GEC74 → JC721OOJE8 → NMCB1OFE44 → NJI41OM874 → NJIC9GE874 → JCA71OJGE8 → NCB61OKFE4 → NJE41OMC74 → NJIC1OE874NJCA1OGE74NJC61OKE74NJEC1OEC74NJC21OOE74NMJC1OE744NJIC1OE874
1199 max steps6000000078C → C875QQQKJIF → LJI83QMI876 → NGEB9QGFCA4 → ME652QNLKC5 → OIHF7QIB983 → NHA95QKHG94 → MIB86QJIF85 → LGBA6QJGFA6 → KF964QLKHB7 → MFDB5QKFDB5 → LH941QOMH96 → PKGC7QIEA62 → OJD83QMID73 → NLFB4QLFB54 → MJGA3QMGA75 → NHF95QKHB94 → MIB85QKIF85 → LHCA6QJGE96 → KFA73QMJGB7 → NFD94QLHDB4 → MJC61QOKE75 → PJGD6QJDA72 → OJC92QNHE73 → OLGA4QLGA53 → NKGB5QKFA64 → MIEA4QLGC85 → MHD83QMID95 → NHE93QMHC94 → NJD84QLID74 → MJEB4QLFC75 → MHE82QNIC95 → OIE94QLHC83 → NKD94QLHD64 → MJFB3QMFB75 → NHF83QMIB94 → NJE95QKHC74 → MIDA4QLGD85 → MHD82QNID95 → OIE93QMHC83 → NLE94QLHC54 → MJGC4QLEA75 → MHE93QMHC95 → NHD84QLID94 → MJD93QMHD75 → NHFA3QMGB94 → NJD74QLJD74 → MJEC5QKEC75 → LHD71QOJD96 → PIEA3QMGC82 → OME83QMIC43 → NLIE5QKC854 → MIGC5QKEA85 → LHC83QMIE96 → NGD94QLHDA4 → MJC72QNJE75 → OIFC6QJEB83 → NIB72QNJF84 → OJGB6QJFA73 → NIC94QLHE84 → MJD94QLHD75 → MHEA3QMGC95 → NHD73QMJD94 → NJFA3QMGB74 → NJF94QLHB74 → MJEA5QKGC75 → LHD93QMHD96 → NGC83QMIEA4 → NJE83QMIC74 → NJFB5QKFB74 → MID83QMID85 → NHEA4QLGC94 → MJC73QMJE75 → NHFC6QJEB94 → MHA62QNKG95 → OIGB6QJFA83 → NIB84QLIF84 → MJDA6QJGD75 → LGC92QNHEA6 → OHC73QMJE93 → NLFA4QLGB54 → MJGB4QLFA75 → MHE94QLHC95 → MHC84QLIE95 → MHD94QLHD95MHC83QMIE95NHE94QLHC94MJC84QLIE75MHEB5QKFC95LHB62QNKF96OHFB5QKFB93NJB63QMKF74NJGD7QIDA74MGC82QNIEA5OIE83QMIC83NLEA5QKGC54MIGA3QMGA85NHE85QKIC94MIC94QLHE85MHD94QLHD95
1280 max steps40000000088O → O883QQQQMII3 → NNII63MK8834 → KKIEA9GGC867 → EDA761OKJGDD → NEC60QQPKEC4 → QMJB7QQIF741 → PMJF82NIB742 → NLICA3MGE854 → KIGA61OKGA87 → NEDA65KKGDC4 → JFE61QQOKCB8 → PKG970PJHA62 → PNEC85KIEC32 → NKFA21OOGB64 → NMJE63MKC744 → KIIEC1OEC887 → NDAA21OOGGD4 → NMJ65QQKK744 → MMIGD0PDA845 → PIHA5QQKG982 → OLHB80PIF953 → PLGA83MIGA52 → NJGA65KKGA74 → JFEC65KKECB8 → FEB421OOMFCC → NMI431ONM844 → NKJII9G88764 → JECAA6JGGEC8 → DB6621OOKKFE → NMEE40PMCC44 → PJII21OO8872 → OMMCA9GGE443 → LII761OKJ886 → NFECA9GGECB4 → J76421OOMKJ8 → NMIECAFEC844 → JIA521OOLG88 → NMGBA5KGFA44 → JIF663MKKB88 → JEEBA3MGFCC8 → JB6421OOMKF8 → NMIEB3MFC844 → KIIA41OMG887 → NIDAA5KGGD84 → JFA65QQKKGB8 → LKCA80PIGE66 → PFEA61OKGCB2 → OME641OMKC43 → NLIIE1OC8854 → NJGAA1OGGA74 → NJC665KKKE74 → JFEEC1OECCB8 → NB4221OOOMF4 → NMMJI3M87444 → KIIIC9GE8887 → DAAA71OJGGGE → NC6660PKKKE4 → PJEEE1OCCC72 → OMC221OOOE43 → NMMLI1O85444 → NJIIG9GA8874 → JCAA75KJGGE8 → FCB661OKKFEC → NEE431ONMCC4 → NKJI21OO8764 → NMJEC9GEC744 → JIC721OOJE88 → NMCBA1OGFE44 → NJI641OMK874 → NJIEC9GEC874 → JCA721OOJGE8 → NMCB61OKFE44 → NJIE41OMC874 → NJICA1OGE874NJCA61OKGE74NJEC61OKEC74NJEC21OOEC74NMJC21OOE744NMJIC1OE8744NJICA1OGE874
13146 max steps30000000009DD → DD92QQQQQNHDE → OHDDD8QHDDD93 → NG83QQQQQMIA4 → NMIGA4QLGA844 → MJID85QKID875 → LHDBA4QLGFD96 → MFC751QOLJEB5 → PJHE82QNIC972 → ONGB94QLHFA33 → NLJC74QLJE754 → MJGEC6QJECA75 → LGC941QOMHEA6 → PKGC73QMJEA62 → OMGD93QMHDA43 → NLID72QNJD854 → OJIEB4QLFC873 → NKEB72QNJFC64 → OJHD82QNID973 → OLGB93QMHFA53 → NLHC74QLJE954 → MJGEA4QLGCA75 → MHE963QMKHC95 → NHGB84QLIFA94 → MJD974QLJHD75 → MHECA3QMGEC95 → NHD741QOMJD94 → PKJFA3QMGB762 → OMGD94QLHDA43 → NKIC72QNJE864 → OJHDB5QKFD973 → NJDA61QOKGD74 → PKHD92QNHD962 → ONHB83QMIF933 → NLKE95QKHC654 → MIGEB4QLFCA85 → MHD852QNLID95 → OIHD93QMHD983 → NLE983QMIHC54 → NJHD94QLHD974 → MJEA83QMIGC75 → NHFB83QMIFB94 → NJE963QMKHC74 → NJGDA4QLGDA74 → MJE962QNKHC75 → OIGDA4QLGDA83 → NKD862QNKID64 → OJHEC4QLEC973 → NKEA51QOLGC64 → PKIFA3QMGB862 → OMGC84QLIEA43 → NKID83QMID864 → NJGCA4QLGEA74 → MJE963QMKHC75 → NHGDA4QLGDA94 → MJC762QNKJE75 → OIGDC6QJEDA83 → NIB840QPMIF84 → QLJEA6QJGC751 → PLFC93QMHEB52 → OMHC62QNKE943 → OLJGB4QLFA753 → NKGE94QLHCA64 → MJFB73QMJFB75 → NHFC83QMIEB94 → NJE962QNKHC74 → OJHDA4QLGD973 → NKEA72QNJGC64 → OJHD93QMHD973 → NLFA83QMIGB54 → NJHD84QLID974 → MJEB93QMHFC75 → NHFA62QNKGB94 → OJHB74QLJF973 → NKECA5QKGEC64 → MIEA41QOMGC85 → PKHE83QMIC962 → OMGC94QLHEA43 → NKIC73QMJE864 → NJGDB5QKFDA74 → MID951QOLHD85 → PJHD93QMHD972 → OMFA83QMIGB43 → NLIE84QLIC854 → MJGDA5QKGDA75 → LHD962QNKHD96 → OHFB83QMIFB93 → NLE963QMKHC54 → NJHFB4QLFB974 → MJEA63QMKGC75 → NHGD93QMHDA94 → NJD872QNJID74 → OJGCB4QLFEA73 → NKE952QNLHC64 → OJIFB4QLFB873 → NKEB73QMJFC64 → NJGD82QNIDA74 → OJGB82QNIFA73 → OLGB84QLIFA53 → NKGD84QLIDA64 → MJFC82QNIEB75 → OIFB72QNJFB83 → OLGB73QMJFA53 → NLHE94QLHC954 → MJGC84QLIEA75 → MHEB83QMIFC95NHE962QNKHC94OJHB84QLIF973NKEB95QKHFC64MIEB62QNKFC85OIGC72QNJEA83OLGB83QMIFA53NLHD84QLID954MJGD93QMHDA75NHFA72QNJGB94OJGA74QLJGA73NKEC95QKHEC64MIEB51QOLFC85PJHD72QNJD972ONGCA3QMGEA33NLKC63QMKE654NJHFE7QICB974MGC962QNKHEA5OIGB73QMJFA83NLFB84QLIFB54MJGD73QMJDA75NHFC92QNHEB94OJE862QNKIC73OLHDB5QKFD953NJGB61QOKFA74PKHD94QLHD962OLFB83QMIFB53NLHD73QMJD954NJHEA3QMGC974NJFA73QMJGB74NJFC94QLHEB74MJEA62QNKGC75OIGD93QMHDA83NLE972QNJHC54OJIEA4QLGC873NKEB83QMIFC64NJGC72QNJEA74OJGC93QMHEA73NLFA73QMJGB54NJHE94QLHC974MJEA84QLIGC75MHEB83QMIFC95