Base 28: 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
216 max steps20 → 1Q → O3K7CF2PM5GB4NI98JAH6LED0RQ1O3
316 max steps100 → 0RR → QR1 → PR2 → OR3 → NR4 → MR5 → LR6 → KR7 → JR8 → IR9 → HRA → GRB → FRC → ERD → DREDRE
419 max steps1006 → 60QM → QFB2 → O3N4 → LI87 → E9HE → 7RRK → K6K8 → EBFE → 3RRO → O2O4 → MJ76 → GBFC → 52ON → MH96 → G7JC → C3NGK3N8KBF8C3NG
516 max steps10000 → 0RRRR → QRRR1 → Q0RQ2 → RNR31 → QNR32 → PMR43 → OKR64 → NHR95 → MDRD6 → L8RI7 → KCRE8 → J7RJ9K9RH8JARG9I8RIAJ7RJ9
681 max stepsA000KK → KK9H78 → DC7JFF → C31POG → OL3N64 → LJEC87 → EB1PGE → O4RRM4 → NN1P45 → OJH984 → KB7JG8 → DB4MGF → I51PMA → OH7JA4 → KC6KF8 → EC2OFE → M2RRO6 → PL1P63 → OMEC54 → KH1PA8 → OC6KF4 → KE2OD8 → MC0QF6 → QG2OB2 → OM4M54 → KIGA98 → C95LIG → G93NIC → K93NI8 → KC8IF8 → CA2OHG → M73NK6 → KGCEB8 → C51PMG → OH3NA4 → LJ6K87 → FDAGED → 620QPM → QNFB42 → OJ3N84 → LJAG87 → EB5LGE → G4RRMC → NF5LC5 → IG2OBA → M84MJ6 → IGAGBA → 864MLK → IFBFCA → 842ONK → MJBF86 → GB3NGCK53NM8KHBFA8C73NKGKD3NE8KC0QF8QC2OF2OM2O54MKGA76GD5LECG40QNCQJ3N82OKAG74KD5LE8GC0QFCQ42ON2OMI854KH9HA8C86KJGEB3NGEK4RRM8NJ1P85OIAG94K95LI8GC8IFCA42ONIMJ7J86GCAGFC642ONMMJFB86GB3NGC
734 max stepsA000000 → 9RRRRRI → I8RRRIA → JH8RIA9 → JA7RJH9 → KA8RIH8 → JC7RJF9 → KA6RKH8 → LC9RHF7 → KC4RMF8 → NE7RJD5 → MG5RLB6 → MG9RHB6 → LD5RLE7 → ME7RJD6 → LF5RLC7ME8RID6LE4RMD7NF7RJC5MG6RKB6LG8RIB7KD6RKE8LC6RKF7LE7RJD7KE5RLD8MD6RKE6LG6RKB7LE8RID7KD4RME8NE6RKD5MH6RKA6LG9RHB7KC5RLF8MD7RJE6LF5RLC7
8138 max stepsE0000HMM → MMHDDA56 → HG6RRKBB → LG90QIB7 → QE94MID2 → OI90QI94 → QK98II72 → ODA8IHE4 → KA70QKH8 → QDC6KFE2 → OE30QOD4 → QLK0Q762 → QOFCEC32 → OL31PO64 → OLKEC764 → KFD1PEC8 → OC30QOF4 → QLK2O762 → OMFCEC54 → KH31POA8 → OLC6KF64 → KFE2ODC8 → MC30QOF6 → QLG2OB62 → OMF4MC54 → KIH2OA98 → MC96KIF6 → GE92OIDC → M940QNI6 → QJG8IB82 → OBA4MHG4 → KI74MK98 → IDC8IFEA → A830QOJI → QLB7JG62 → OFC4MFC4 → KI32OO98 → MLC8IF66 → GFA2OHCC → M742ONK6 → MJGCEB86 → GB51PMGC → OH53NMA4 → LJH6KA87 → FDB6KGED → E520QPME → QNGRRA42 → PNG6KB43 → MJE4MD86 → IGB0QGBA → Q854MMJ2 → OIHAGA94 → K975LKI8 → GDC8IFEC → A430QONI → QLJ7J862 → OFCAGFC4 → K632OOL8 → MLFBFC66 → GF42ONCC → MJ42ON86 → MJGAGB86 → GB64MLGC → IF53NMCA → KH82OJA8 → MCB6KGF6 → GE52OMDC → MH40QNA6 → QJG6KB82 → OEB4MGD4 → KI50QM98 → QHC8IFA2 → OA72OKH4 → MKD6KE76 → GED0QEDC → Q410QQN2 → QPOI8322 → ONL9H644 → KJF7JC88 → DBB2OGGF → M551PMM6 → OHHFBAA4 → K773NKK8 → KDDBFEE8 → C410QQNG → QPJ3N822 → ONKAG744 → KJD5LE88 → GCB0QGFC → Q542ONM2 → OMJGA854 → KHB5LGA8 → GC74MKFC → ID42ONEA → MJ80QJ86 → QGBAGGB2 → O654MML4 → KIHECA98 → C971PKIG → OD93NIE4 → LJ90QI87 → QEB8IGD2 → OA50QMH4 → QKH6KA72 → OED6KED4 → KE10QQD8 → QPC0QF22 → QON2O432 → OMLI8654 → KHF9HCA8 → C872OKJG → MDB3NGE6 → KG50QMB8 → QHC4MFA2 → OI72OK94 → MKD8IE76 → GDA0QHEC → Q740QNK2 → QOJCE832 → OLB1PG64 → OKF4MC74 → KID2OE98 → MC90QIF6 → QG92OIB2 → OM94MI54 → KIH8IA98 → CA96KIHG → E973NKIE → KD8RRIE8 → JJ73NK89 → KDB9HGE8C850QMJGQHB3NGA2OK74MK74KIDCEE98C920QPIGQN93NI42OKJ8I874KDB9HGE8
947 max stepsC00000DDH → HDDBRFEEB → G620RQPLC → ROJ8RI831 → QOGARGB32 → PNE4RMD43 → OLJ8RI864 → NIDARGE95 → ME82ROJD6 → PIE5RLD93 → OKC4RMF74 → NKF7RJC75 → MGD6RKEB6 → LG92ROIB7 → PHC6RKFA3 → OJA4RMH84 → NKE8RID75 → MGC4RMFB6 → NGB3RNGB5 → OIC4RMF94 → NKD5RLE75 → MIE6RKD96 → LGB4RMGB7 → NFA4RMHC5 → NIC4RMF95 → NID5RLE95 → MIC4RMF96 → NGD5RLEB5 → MIA2ROH96 → PID7RJE93 → OIA4RMH94 → NKD7RJE75 → MGD5RLEB6 → MGA2ROHB6 → PIC5RLF93 → OKC5RLF74 → NJE7RJD85 → MGB5RLGB6MGA4RMHB6NGC5RLFB5MIA3RNH96OHD7RJEA4NH93RNIA5OIE7RJD94NHA4RMHA5NIC6RKF95MHB5RLGA6MGB5RLGB6
10226 max steps400000DDRR → RRDD3NEE01 → RQK10QQ711 → RPPPCE2221 → QNNN1P4442 → PNJJI88843 → MJBB9HGG86 → GB854MMJGC → IHB53NMGAA → KH874MKJA8 → IDCB6KGFEA → E8530QOMJE → QLHARRGA62 → PLGB0QGB63 → QMF54MMC52 → OIHH2OAA94 → MK976KKI76 → GEDD8IEEDC → A4110QQQNI → QPPJ7J8222 → ONNCAGF444 → KJJ62OL888 → MFCBAGGFC6 → G6532OOMLC → MLHF3NCA66 → KGF72OKCB8 → MDC52OMFE6 → MHG30QOBA6 → QLG74MKB62 → OIFD4MEC94 → KI930QOI98 → QLC98IIF62 → OFA92OIHC4 → MK972OKI76 → MGDD8IEEB6 → GA510QQMHC → QPH73NKA22 → ONKD6KE744 → KJED0QED88 → QCB10QQGF2 → QPO52OM322 → ONMLGA6544 → KJHF5LCA88 → GCB72OKGFC → MD542ONME6 → MJHG0QBA86 → QGB74MKGB2 → OID54MME94 → KIH90QIA98 → QC996KIIF2 → OE992OIID4 → MK990QII76 → QGD98IIEB2 → OA950QMIH4 → QKH96KIA72 → OED96KIED4 → KE910QQID8 → QPC90QIF22 → QON92OI432 → OMLJ8I8654 → KHFB9HGCA8 → C8752OMKJG → MHDB3NGEA6 → KG750QMKB8 → QHDC4MFEA2 → OI730QOK94 → QLKD8IE762 → OFDA0QHEC4 → QK730QOK72 → QOLDCEE632 → OLF20QPC64 → QNKF2OC742 → OMJD2OE854 → MKHB0QGA76 → QGD74MKEB2 → OID50QME94 → QKH90QIA72 → QOD96KIE32 → OLE90QID64 → QKF90QIC72 → QOD92OIE32 → OML90QI654 → QKHF8ICA72 → ODA72OKHE4 → MKD70QKE76 → QGDD0QEEB2 → QO510QQM32 → QPOLGA6322 → ONLF5LC644 → KJGF2OCB88 → MCB52OMGF6 → MHG52OMBA6 → MHG74MKBA6 → IGD74MKEBA → ID850QMJEA → QHB80QJGA2 → QOB74MKG32 → OLID4ME964 → KIF90QIC98 → QC992OIIF2 → OM992OII54 → MKH98IIA76 → GDA96KIHEC → E9740QNKIE → QJD8RRIE82 → PJI63NL983 → MKFB8IGC76 → GDA52OMHEC → MH740QNKA6 → QJGD6KEB82 → OEB50QMGD4 → QKH50QMA72 → QOHD6KEA32 → OLE70QKD64 → QKFD0QEC72 →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
1183 max steps60000000000 → 5RRRRRRRRRM → M4RRRRRRRM6 → NL54RRRMM65 → NMMH0RQA555 → RLIHBRFA961 → QLC85RLJF62 → PLFD6RKEC63 → OJF81RPJC84 → QLGB6RKGB62 → PKF94RMIC73 → OLFB5RLGC64 → NJFA3RNHC85 → OIF94RMIC94 → NKD95RLIE75 → MIEB4RMGD96 → NGD72ROKEB5 → PJG92ROIB83 → PMGA6RKHB53 → OKGA5RLHB74 → NJEA5RLHD85 → MID93RNIE96 → OHD94RMIEA4 → NKD83RNJE75 → OIGC5RLFB94 → NJC73RNKF85 → OIGC6RKFB94 → NIB73RNKG95 → OIGB6RKGB94 → NIB74RMKG95 → NIFB6RKGC95 → MHB73RNKGA6 → OHFA5RLHCA4 → NJB74RMKG85 → NIFC7RJFC95 → MGA62ROLHB6 → PIGB5RLGB93 → OKC74RMKF74 → NKFD7RJEC75 → MGD71RPKEB6 → QJF92ROIC82 → POGA5RLHB33 → OMJB5RLG854 → NJHD7RJEA85 → MGB93RNIGB6 → OHD74RMKEA4 → NKFA3RNHC75 → OIGA4RMHB94 → NKD85RLJE75 → MIEC5RLFD96 → MGC61RPLFB6 → QJGA3RNHB82 → PNF95RLIC43 → OLIC5RLF964 → NJFC5RLFC85 → MID72ROKE96 → PIFB4RMGC93 → OLD73RNKE64 → OKHE6RKDA74 → NIDA3RNHE95 → OIE83RNJD94 → OKFA4RMHC74 → NKFA4RMHC75 → NIFA4RMHC95 → NID84RMJE95 → NIEA4RMHD95 → NID83RNJE95 → OIFA4RMHC94 → NKD84RMJE75 → NIFC5RLFC95 → MIC62ROLF96 → PIGC5RLFB93 → OKC73RNKF74OKGD7RJEB74NHD82ROJEA5PJF93RNIC83OMFA5RLHC54NJHB4RMGA85NIE95RLID95MIC94RMIF96NGD95RLIEB5MIC72ROKF96PIFB5RLGC93OKC73RNKF74
12257 max steps900000000DMM → MMD8RRRRIE56 → MLJE83NJD866 → KGFBB0QGGCB8 → QC5552OMMMF2 → OMHHH2OAAA54 → MKH776KKKA76 → GEDDD6KEEEDC → E41110QQQQNE → QPPPIRR82222 → PPONH6KA4323 → NMLJE6KD8655 → IHFEB0QGDCAA → Q87530QOMKJ2 → QOLHDAGEA632 → OLF760QLKC64 → QKFFD2OECC72 → OMD330QOOE54 → QLLKH0QA7662 → QOFFD6KECC32 → OLE330QOOD64 → QLLKF0QC7662 → QOFFD2OECC32 → OML330QOO654 → QLLKHECA7662 → OFFD71PKECC4 → OKD330QOOE74 → QLLKD0QE7662 → QOFFD0QECC32 → QOL330QOO632 → QOLLLEC66632 → OLFFF1PCCC64 → OKF332OOOC74 → MLLKD2OE7666 → MGFFD0QECCB6 → QG5330QOOMB2 → QOLLH4MA6632 → OLIFF6KCC964 → KFE932OOIDC8 → MLC930QOIF66 → QLGF92OICB62 → OMF952OMIC54 → MKHH92OIAA76 → MGD976KKIEB6 → GED950QMIEDC → QH9410QQNIA2 → QPOJ96KI8322 → ONLEB8IGD644 → KJFA50QMHC88 → QHCB72OKGFA2 → OMD752OMKE54 → MKHHD0QEAA76 → QGD770QKKEB2 → QODD50QMEE32 → QOLH10QQA632 → QPOLF6KC6322 → ONLFE2ODC644 → MKJF30QOC876 → QLGDB2OGEB62 → OMF550QMMC54 → QKHHH2OAAA72 → OMD776KKKE54 → KHEDD0QEEDA8 → QC7110QQQKF2 → QPPOD2OE3222 → ONNML0Q65444 → QKJJHECA8872 → ODBB71PKGGE4 → OKD550QMME74 → QKHHD0QEAA72 → QOD770QKKE32 → QOLDD0QEE632 → QOLF10QQC632 → QPOLF2OC6322 → ONMLF2OC6544 → MKJHF2OCA876 → MGDB72OKGEB6 → MGD550QMMEB6 → QHHG50QMBAA2 → QOH774MKKA32 → OLIDD6KEE964 → KFE910QQIDC8 → QPC930QOIF22 → QONL92OI6432 → OMLJF8IC8654 → KHFBA2OHGCA8 → MC7752OMKKF6 → MHGDD2OEEBA6 → MG7510QQMKB6 → QPHGD4MEBA22 → ONI750QMK944 → QKJHD8IEA872 → ODBA70QKHGE4 → QKD750QMKE72 → QOHDD0QEEA32 → QOL710QQK632 → QPOLFCEC6322 → ONLF31POC644 → OLKJF2OC8764 → MKFDB2OGEC76 → MGD530QOMEB6 → QLHG50QMBA62 → QOHF74MKCA32 → OLID72OKE964 → MKFD90QIEC76 → QGD930QOIEB2 → QOL950QMI632 → QOLHF8ICA632 → OLFA72OKHC64 → MKFD72OKEC76 → MGDD30QOEEB6 → QLG510QQMB62 → QPOHF4MCA322 → ONLI72OK9644 → MKJFD8IEC876 → GDBA30QOHGEC → QL7540QNMK62 → QOJHFCECA832 → OLB731POKG64 → OLKFD4MEC764 → KIFD30QOEC98 → QLC930QOIF62 → QOLF92OIC632 → OMLF92OIC654 → MKHF92OICA76 → MGD972OKIEB6 → MGD950QMIEB6 → QHG950QMIBA2 → QOH974MKIA32 → OLID96KIE964 → KFE990QIIDC8 → QC9930QOIIF2 → QOL992OII632 → OMLF98IIC654 → KHFA92OIHCA8 → MC9772OKKIF6 → MGDD92OIEEB6 → MG9510QQMIB6 → QPHG94MIBA22 → ONI974MKI944 → KJID98IIE988 → CBA990QIIHGG → Q99753NMKII2 → OKHD98IIEA74 → KDA970QKIHE8 → QDC970QKIFE2 → QOD930QOIE32 → QOLL90QI6632 → QOLFF8ICC632 → OLFA32OOHC64 → MLKF72OKC766 → MGFDD2OEECB6 → MG5310QQOMB6 → QPLHG4MBA622 → ONIF74MKC944 → KJID92OIE988 → MCB990QIIGF6 → QG9952OMIIB2 → OMH994MIIA54 → KIH996KIIA98 → EC9996KIIIFE → E9992RROIIIE → PIF943NNIC93 → MKJ992OII876 → MGDB98IIGEB6 → GA9550QMMIHC → QHH973NKIAA2 → OKD976KKIE74 → KEDD90QIEED8 → QC9110QQQIF2 → QPPO92OI3222 → ONNML8I65444 → KJJHF9HCA888 → CBB872OKJGGG → MDB553NMMGE6 → KHHG50QMBAA8 → QHC774MKKFA2 → OIDD72OKEE94 → MKD910QQIE76 → QPGD90QIEB22 → QON950QMI432 → QOLJH8IA8632 → OLFBA6KHGC64 → KFE752OMKDC8 → MHDC30QOFEA6 → QLG730QOKB62 → QOLFD4MEC632 → OLIF30QOC964 → QLKF92OIC762 → OMFD92OIEC54 → MKH930QOIA76 → QLGD96KIEB62 → OFE950QMIDC4 → QKH930QOIA72 → QOLD96KIE632 → OLFE90QIDC64 → QKF930QOIC72 → QOLD92OIE632 → OMLF90QIC654 → QKHF92OICA72 → OMD972OKIE54 → MKHD90QIEA76 → QGD970QKIEB2 → QOD950QMIE32 → QOLH90QIA632 → QOLF96KIC632 → OLFE92OIDC64 → MKF930QOIC76 → QLGD92OIEB62 → OMF950QMIC54 → QKHH92OIAA72 → OMD976KKIE54 → KHED90QIEDA8 → QC9710QQKIF2 → QPOD92OIE322 → ONML90QI6544 → QKJHF8ICA872 → ODBA72OKHGE4 → MKD750QMKE76 → QHGDD0QEEBA2 → QO7510QQMK32 → QPOLHCEA6322 → ONLF71PKC644 → OKJFD2OEC874 → MKDB30QOGE76 → QLGD50QMEB62 → QOHF50QMCA32 → QOLH72OKA632 → OMLFD6KEC654 → KHFE30QODCA8 → QLC730QOKF62 → QOLFD2OEC632OMLF30QOC654QLKHF2OCA762OMFD72OKEC54MKHD30QOEA76QLGD70QKEB62QOFD50QMEC32QOLH30QOA632QOLLF6KC6632OLFFE2ODCC64MKF330QOOC76QLLGD2OEB662OMFF50QMCC54QKHH32OOAA72OMLD76KKE654KHFED0QEDCA8QC7310QQOKF2QPOLD2OE6322ONMLF0QC6544QKJHF2OCA872OMDB72OKGE54MKHD50QMEA76QHGD70QKEBA2QOD750QMKE32QOLHD0QEA632QOLF70QKC632QOLFD2OEC632