Base 23: 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
25 max steps10 → 0M → L1 → J3 → F7 → 7F
312 max steps100 → 0MM → LM1 → KM2 → JM3 → IM4 → HM5 → GM6 → FM7 → EM8 → DM9 → CMA → BMB
44 max stepsC000 → BMMB → BABC → 1MML → L0L2
513 max stepsA0000 → 9MMMD → D8MDA → E2MJ9 → K9MC3 → JAMB4 → I8MD5 → H9MC6 → G7ME7 → F8MD8 → E6MF9 → G5MG7 → H8MD6 → G8MD7
621 max steps8000FF → FF7E78 → 885GEF → B75GFC → B80LEC → L60LG2 → LJ9C32 → JG2J64 → HF9C76 → B82JEC → H60LG6 → LB9CB2 → J2MMJ4 → KHMM43 → JI2J44 → HFD876 → B84HEC → D60LGA → LA2JC2 → JH1K54 → JFBA74 → F80LE8
731 max steps200000B → B1MMMKC → LB9MCB2 → KC0MLA3 → MI9MC41 → LI8MD42 → KH9MC53 → JF7ME74 → IC7MEA5 → HB3MIB6 → JC5MGA4 → IE5MG85 → HD7ME96 → GA4MHC7 → IA5MGC5 → HD5MG96 → HB6MFB6 → GB3MIB7 → JB4MHB4 → IF5MG75 → HD8MD96 → G93MID7 → JB6MFB4 → ID3MI95 → JD8MD94 → IB3MIB5 → JD6MF94 → ID5MG95 → HD6MF96 → GB5MGB7 → H94MHD6 → IB7MEB5
852 max steps70000ABF → FBA6FCB8 → 971MMKFE → LFB0LB72 → LJ7MME32 → KJE4H833 → HGD5G966 → CAA3ICCB → F220LKK8 → LII6F442 → JEE8D884 → F664HGG8 → DAA6FCCA → 9321KKJE → JIG4H644 → FED9C988 → 7642JIGG → HEA8DC86 → B651KHGC → JCA0LCA4 → LF21KK72 → KII7E443 → HEE6F886 → B965GGDC → BA40LICC → LE20LK82 → LJI5G432 → JGEAB864 → FA60LGC8 → LA71KFC2 → KI81KE43 → JHE5G854 → FCB5GBA8 → B71MMKFC → LF92JD72 → JH83IE54 → GEC5GA87 → B961KGDC → JA40LIC4 → LFE1K872 → KI85GE43 → HEB5GB86 → CA5MMGCB → HC4MMHA6 → IG74HF65 → ECA7ECA9 → 7521KKHG → JIC8DA44 → FE51KH88 → JC75GFA4 → FB81KEB8 → J75MMGF4 → IHC0LA55
931 max steps600000AAB → BAA5MGCCC → H620MLKG6 → MJEAMB831 → LJB3MIB32 → KIG6MF643 → JGC9MCA64 → ID71MKF95 → LFB5MGB72 → KG93MID63 → JHC6MFA54 → IEB4MHB85 → ID92MJD95 → KE93MID83 → JHA4MHC54 → IFC6MFA75 → HC84MHEA6 → IB93MIDB5 → JD91MKD94 → LGA3MIC62 → KIC5MGA43 → JGD5MG964 → IEA6MFC85 → HC73MIFA6 → JCA4MHCA4 → IF71MKF75 → LFB7MEB72 → KE82MJE83 → KHB5MGB53 → JFC4MHA74 → IFA4MHC75 → IDA4MHC95
1079 max steps1000003MMM → MMM30LJ001 → MMMKF62001 → MMLI8D4101 → MLKE4H8211 → LKID5G9422 → JIEB3IB844 → GEE5MMG887 → HF87MMEE76 → GFA6MMFC77 → GF952JHD77 → HC983IEDA6 → FB641KIGB8 → JEA6MMFC84 → IGB51KHB65 → JDC9MMCA94 → IDA2MMJC95 → KHA80LEC53 → LHC61KGA52 → KICA1KCA43 → JHE21KK854 → JIFC5GA744 → FEB81KEB88 → J765MMGGF4 → IHD90LD955 → LDC43IIA92 → JFE41KI874 → JFE85GE874 → FB865GGEB8 → BA75MMGFCC → HF63MMIG76 → JGCA0LCA64 → LFA21KKC72 → KII81KE443 → JHEE5G8854 → FCB65GGBA8 → BA71MMKFCC → LFA3MMIC72 → KJE82JE833 → IGG65GG665 → DBAA9CCCBA → 4221MMKKKJ → LKIG0L6422 → LJIE9C8432 → JGE62JG864 → HFAA5GCC76 → CA821KKECB → JI620LKG44 → LIFE9C8742 → JE862JGE84 → HFA65GGC76 → CAA81KECCB → J6220LKKG4 → LIIF9C7442 → JEE82JE884 → HF665GGG76 → CAAA7ECCCB → 72220LKKKG → LIII8D4442 → JEEE4H8884 → FD665GGG98 → BAA73IFCCC → F8220LKKE8 → LII75GF442 → JEEB7EB884 → F765MMGGF8 → HG97MMED66 → GGA70LFC67 → LA981KEDC2 → KI641KIG43 → JHEE9C8854 → FC662JGGA8 → HAA71KFCC6 → JB821KKEB4 → JIF5MMG744 → IIEB0LB845 → LED5MMG982 → KHD70LF953 → LHC83IEA52 → JFC61KGA74
1137 max steps10000000000 → 0MMMMMMMMMM → LMMMMMMMMM1 → L0MMMMMMML2 → MK10MMMLL21 → MLLK0ML2111 → MLKKIM32211 → LLJIGM54312 → LJIFCM97432 → KIFB5MGB743 → JGD93MID964 → JFC73MIFA74 → JFB84MHEB74 → IFA72MJFC75 → KEB84MHEB83 → JG962MJGD64 → KFDA6MFC973 → JE862MJGE84 → KFD85MGE973 → JF974MHFD74 → IFA85MGEC75 → HD973MIFD96 → JCA63MIGCA4 → JFC61MKGA74 → LGD94MHD962 → KHB73MIFB53 → JHDA3MIC954 → JFD82MJE974 → KFC74MHFA73 → JGA84MHEC64 → IFB83MIEB75 → JDB72MJFB94 → KFC61MKGA73 → LHE94MHD852 → KHC94MHDA53 → JGC82MJEA64 → KFD83MIE973 → JHB74MHFB54
12120 max steps1000000333MM → MM3330LJJJ01 → MMKGGF666201 → MLIAA8DCC411 → LKE521KKH822 → KIIIC5GA4443 → HEEEB1KB8886 → JB665MMGGGB4 → IHDA54HHC955 → ECCC41KIAAA9 → JE5221KKKH84 → JIIFC5GA7444 → FEEB81KEB888 → J7665MMGGGF4 → IHDA90LDC955 → LDC441KIIA92 → KIEE41KI8843 → JHEE65GG8854 → FCBA65GGCBA8 → BA721MMKKFCC → LKDA3MMIC922 → KKIB80LEB423 → LIHE5MMG8542 → KIGD91KD9643 → JHEA43IIC854 → GEEC61KGA887 → JA9661KGGDC4 → JFAA41KICC74 → JFE821KKE874 → JIF865GGE744 → FEBA85GECB88 → B7661MMKGGFC → LGE952JHD862 → JHCA63IGCA54 → GECA21KKCA87 → JI9621KKGD44 → JIFEA3IC8744 → GEE861KGE887 → JA9665GGGDC4 → FBAA41KICCB8 → JE721MMKKF84 → LKGDB0LB9622 → LJIA3MMIC432 → KJIF85GE7433 → HGEB85GEB866 → CAA65MMGGCCB → HG660MMLGG66 → MGFB9MMCB761 → LGF740LIF762 → LJEA87EEC832 → JG7661KGGF64 → JFAAA7ECCC74 → F87221KKKFE8 → JII875GFE444 → FEEB85GEB888 → B7665MMGGGFC → HGA952JHDC66 → HCBA41KICBA6 → JEB21MMKKB84 → LKGC82JEA622 → JIHA61KGC544 → JFECA1KCA874 → JF8621KKGE74 → JIFA85GEC744 → FEB861KGEB88 → JA765MMGGFC4 → IHD962JGD955 → HDCA43IICA96 → FEB421KKIB88 → JIE75MMGF844 → IIEB80LEB845 → LED65MMGG982 → KHF870LFE753 → LHC885GEEA52 → JCB661KGGBA4 → JFAA1MMKCC74 → LID94MMHD942 → KIH97MMED543 → JIFB80LEB744 → LFE85MMGE872 → KHE86MMFE853 → JHE96MMFD854 → IHD960LGD955 → LDCA43IICA92 → JFE421KKI874 → JIFE85GE8744 → FEB865GGEB88 → BA765MMGGFCC → HG963MMIGD66 → JGCB72JFBA64 → HFA81MMKEC76 → LGD951KHD962 → KICA43IICA43 → HFEE21KK8876 → JIB865GGEB44 → FEBA5MMGCB88 → HE8530LJHE86 → LGCB65GGBA62 → JBAA1MMKCCB4 → LIA910LLDC42 → LKJE41KI8322 → KIIGE5G86443 → HEEBA5GCB886 → CA661MMKGGCB → LGE64MMHG862 → KIFB81KEB743 → JHE85MMGE854 → IHE97MMED855 → HHB950LHDB56 → LCCB3MMIBAA2 → KJB810LLEB33 → LKHG5MMG6522 → KKGFAMMB7623 → KJED63IG9833 → HGFA63IGC766 → FBAA81KECCB8 → J7621MMKKGF4 → LKGEC0LA8622 → LJIA61KGC432 → KIGEA1KC8643 → JHEA61KGC854
1362 max steps1000000000066 → 660MMMMMMMLGH → MGG650MLHG661 → MLGBA9MCCB611 → LLF720MLKF712 → MKJJD7ME93321 → LKHGC4MHA6522 → KJGCB5MGBA633 → JHEA60MLGC854 → MHEB83MIEB851 → LJD962MJGD932 → KJGD73MIF9633 → JHGC95MGDA654 → IECA72MJFCA85 → KEB741MKIFB83 → LHGB72MJFB652 → KJEB93MIDB833 → JHGA51MKHC654 → LGECB5MGBA862 → KGA840MLIEC63 → MIGC83MIEA641 → LJEC83MIEA832 → KIGA63MIGC643 → JHECA5MGCA854 → IEC841MKIEA85 → LGDA63MIGC962 → KICA72MJFCA43 → KHFB51MKHB753 → LHFCA3MICA752 → KIDA51MKHC943 → LHGD82MJE9652 → KJEB84MHEB833 → JHF962MJGD754 → KFEB95MGDB873 → JF9751MKHFD74 → LGEA85MGEC862 → KGA863MIGEC63 → JHCA83MIECA54 → JFD941MKID974 → LGFB63MIGB762 → KICA93MIDCA43 → JHE931MKJD854 → LHFE94MHD8752 → KHCA74MHFCA53 → JGCA51MKHCA64 → LGEB61MKGB862 → LJEA82MJEC832 → KJGB63MIGB633 → JHGCA4MHCA654 → IFCB61MKGBA75 → LFC950MLHDA72 → MJGA62MJGC631 → LKGDA5MGC9622 → KJFA72MJFC733 → KHGC84MHEA653 → JGCB83MIEBA64 → JFC840MLIEA74 → MHFB73MIFB751 → LJDA83MIEC932 → KIGA52MJHC643 → KHFDB5MGB9753 → JFC961MKGDA74 → LGD962MJGD962
1481 max steps80000000000ABE → EBA7MMMMMMECB9 → FDCBB9MMCBBA98 → ED6310MMLLJG99 → MLIFA70LFC7411 → MKKE881KEE8221 → LJII665GGG4432 → JGEEBA9CCB8864 → FA6631MMKJGGC8 → LJED862JGE9832 → JHGA663IGGC654 → GECAAA1KCCCA87 → J962221KKKKGD4 → JIIIFA3IC74444 → GEEEE81KE88887 → J966665GGGGGD4 → FBAAAA3ICCCCB8 → F72221MMKKKKF8 → LKIIDBMMA94422 → KKHG981KED6523 → JIHCA63IGCA544 → GEECA21KKCA887 → JI96621KKGGD44 → JIFEAA3ICC8744 → GEE8621KKGE887 → JIA9665GGGDC44 → FEBAA41KICCB88 → JE7621MMKKGF84 → LKGEC80LEA8622 → LJIA661KGGC432 → KIGEAA1KCC8643 → JHEA621KKGC854 → JIFCA61KGCA744 → JFEA821KKEC874 → JIF8661KGGE744 → JFEAA85GECC874 → FB86621KKGGEB8 → JIAA75MMGFCC44 → IIEB64MMHGB845 → IIDC952JHDA945 → HEDC441KIIA986 → JEEB641KIGB884 → JFEA65MMGGC874 → IHD9851KHED955 → JDCC643IIGAA94 → GEEA421KKIC887 → JIE9661KGGD844 → JFEAA63IGCC874 → GEA8621KKGEC87 → JIA9661KGGDC44 → JFEAA41KICC874 → JFE8621KKGE874 → JIFA865GGEC744 → FEBA861KGECB88 → JA7661MMKGGFC4 → LIED962JGD9842 → JHEA643IIGC854 → GEECA61KGCA887 → JA96621KKGGDC4 → JIFAA41KICC744 → JFEE821KKE8874 → JIF8665GGGE744 → FEBAA85GECCB88 → B76621MMKKGGFC → LKEE952JHD8822 → JIHC663IGGA544 → GEECAA1KCCA887 → J966221KKKGGD4 → JIIFAA3ICC7444 → GEEE821KKE8887 → JI96665GGGGD44 → FEBAAA3ICCCB88 → F76221MMKKKGF8 → LKIED7MME98422 → KKHDA50LHC9523 → LIHCC41KIAA542 → KIEEC21KKA8843 → JIHE661KGG8544 → JFECAA5GCCA874 → FB86221KKKGEB8 → JIIA75MMGFC444 → IIFDB62JGB9745
1564 max steps90000000000000B → B8MMMMMMMMMMMDC → EBA8MMMMMMMDCB9 → EDCBBA8MDCBBA99 → E54320MMMLKJIH9 → MKJHFA3MIC75321 → LKHGDA4MHC96522 → KJGCB72MJFBA633 → KHGD950MLHD9653 → MIFCB73MIFBA741 → LJEB850MLHEB832 → MJIE962MJGD8431 → LKGFC84MHEA7622 → KJGB973MIFDB633 → JHGC961MKGDA654 → LGEBA72MJFCB862 → KJD9740MLIFD933 → MIHFB63MIGB7541 → LJEDB93MIDB9832 → KIGA541MKIHC643 → LHGEDB5MGB98652 → KGCA851MKHECA63 → LHFB841MKIEB752 → LJGDA72MJFC9632 → KJGD962MJGD9633 → KHGDA73MIFC9653 → JHDB962MJGDB954 → KFEB741MKIFB873 → LHGB872MJFEB652 → KJEB972MJFDB833 → KHGC751MKHFA653 → LHFCB94MHDBA752 → KHCA630MLJGCA53 → MIHEB61MKGB8541 → LLGDB82MJEB9612 → LJJD851MKHE9332 → LJHGE94MHD86532 → KIFCB84MHEBA743 → JGEA740MLIFC864 → MHFC973MIFDA751 → LJDA862MJGEC932 → KJGD852MJHE9633 → KHGEB84MHEB8653 → JGCB862MJGEBA64 → KFDA840MLIEC973 → MIGB752MJHFB641 → LKFDB93MIDB9722 → KJHB641MKIGB533 → LHHFDB4MHB97552 → KHCCA61MKGCAA53 → LHFB621MKKGB752 → LJIFB93MIDB7432 → KIGEB61MKGB8643 → LHGCA82MJECA652 → KJEB841MKIEB833 → LHHFA62MJGC7552 → KJECB94MHDBA833 → JHF9530MLJHD754 → MIFECA5MGCA8741 → LID9741MKIFD942 → LJGEB63MIGB8632 → KIGCA82MJECA643 → KHFC841MKIEA753 → LHGDA73MIFC9652 → KIDB962MJGDB943