Base 27: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
24 max steps10 → 0Q → P1 → N3 → J7
314 max steps100 → 0QQ → PQ1 → OQ2 → NQ3 → MQ4 → LQ5 → KQ6 → JQ7 → IQ8 → HQ9 → GQA → FQB → EQC → DQD
44 max stepsE000 → DQQD → DCDE → 1QQP → P0P2
518 max steps10000 → 0QQQQ → PQQQ1 → P0QP2 → QMQ31 → PMQ32 → OLQ43 → NJQ64 → MGQ95 → LCQD6 → K8QH7 → JBQE8 → I7QI9 → J8QH8 → IAQF9 → H7QIA → J7QI8 → JAQF8 → I8QH9
633 max steps5000PP → PP4L12 → ONG933 → LK6J66 → FECDCC → 320POO → PMK542 → NIEB84 → JA2NG8 → LB5KF6 → GE3MCB → J51OL8 → NGAFA4 → J64LK8 → HEAFCA → 751OLK → NGCDA4 → J60PK8 → PEAFC2 → N51OL4 → NJFA74 → JC4LE8 → HB1OFA → N73MJ4 → KIBE87 → DA2NGE → L60PK6 → PFDCB2 → N40PM4 → PJH872 → NC8HE4 → J91OH8 → NB7IF4 → JB3MF8
730 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 → LD8QHD6
842 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 → JB41OMF8
935 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 → MHC6QJE95
1083 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 → NJIC1OE874
1184 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 → MHD94QLHD95
1274 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 → NJICA1OGE874
13105 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 → MHEB83QMIFC95