Base 18: 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
211 max steps20 → 1G → E3A72FC56B4D890HG1E3
311 max steps100 → 0HH → GH1 → FH2 → EH3 → DH4 → CH5 → BH6 → AH7 → 9H8 → 8H98H9
410 max steps2007 → 71FB → E3D4 → B887 → 3HHE → E2E4 → C976 → 61FCE5B4A5B861FC
514 max steps70009 → 96HA9 → B0HG7 → H8H81 → G8H82 → F7H93 → E7H94 → D6HA5 → C6HA6 → B5HB7 → C3HD6 → E6HA4 → D7H95 → C5HB6C5HB6
637 max steps300039 → 932EE9 → CAHH66 → BB1F67 → E53DC4 → B96A87 → 530GED → GB7962 → E51FC4 → EA6A74 → A42ED8 → C91F86 → E60GB4 → GA4C72 → E82E94 → CA0G76 → G62EB2 → EC4C54 → A86A98 → 420GFE → GD9742 → E91F84 → EA0G74 → GA2E72 → EC2E54 → CA6A76 → 642EDC → C95B86 → 750GCB → G73DA2 → EA2E74CA2E76C62EB6C64CB6864CBA851FCAE71FA4EA2E74
723 max steps1000000 → 0HHHHHH → GHHHHH1 → G0HHHG2 → HF0HG21 → HGDH311 → GGCH412 → GEBH532 → FD8H843 → EB4HC64 → DA5HB75 → C83HD96 → E73HDA4 → EA5HB74 → D93HD85 → E84HC94 → DA3HD75 → E85HB94 → D92HE85 → F94HC83EB3HD64EA6HA74D82HE95F94HC83
875 max steps20000669 → 9661FBB9 → E54HHCC4 → DD8HH845 → DC54CC55 → 9776AAA9 → 432HHEEE → FE9HH733 → EE84C934 → BA80G977 → G430GED2 → GEB88632 → EB4HHC64 → DD80G945 → G980G982 → GE10GG32 → GFEA6322 → EDB3D644 → B994C887 → 8410GGDA → GF91F822 → FDD0G443 → GC988852 → E70HHGA4 → HD93D841 → GA90G872 → GE30GE32 → GEBA6632 → EB53DC64 → B974CA87 → 8430GEDA → GB91F862 → FD50GC43 → GC96A852 → E740GDA4 → GA92E872 → EC30GE54 → GBA6A762 → E542EDC4 → CA96A876 → 6430GEDC → GB95B862 → E650GCB4 → GA74CA72E832EE94CBA0G766G652ECB2EC74CA54A872EA98C320GFE6GDB5B642E964CB84A850GC98G720GFA2GED2E432ECB88654A74HHCA8DA3HHD75EC62EB54CA74CA768632EEBACB51FC66E764CBA4A852EC98C720GFA6GD62EB42EC94C854A870GA98G320GFE2GEDA6432EB93D864B950GC87G740GDA2GE92E832ECB0G654GA74CA72
944 max steps500000000 → 4HHHHHHHD → D3HHHHHD5 → EC43HDD54 → EA97H9874 → D730HGEA5 → HD95HB841 → GD82HE942 → FEA4HC733 → ECA4HC754 → DA74HCA75 → D852HEC95 → F983HD983 → EC50HGC54 → HC96HA851 → GC61HFB52 → GEA5HB732 → FD93HD843 → EC94HC854 → DA73HDA75 → E862HEB94 → FA82HE973 → FC71HFA53 → GCA4HC752 → FC74HCA53 → EB74HCA64 → DA63HDB75 → E873HDA94 → EA61HFB74 → GB83HD962 → FD72HEA43 → FCA5HB753 → EA73HDA74EA62HEB74FA83HD973EC61HFB54GB95HB862FB52HEC63FC95HB853EA72HEA74FA72HEA73FC72HEA53FC94HC853EB73HDA64EA73HDA74
1090 max steps3000003889 → 98832EE999 → CB10HHGG66 → HGAA0G7711 → HFF32EE221 → GDDCA65442 → E9973DA884 → B9310GGE87 → GFB40GD622 → GED94C8432 → EB980G9864 → GA510GGC72 → GFE72EA322 → EDCB2E6544 → CA974CA876 → 86330GEEBA → GBB51FC662 → FD754CCA43 → C9872EA986 → C6310GGEB6 → GFB64CB622 → ED854CC944 → A9870GA988 → G3210GGFE2 → GFEDA64322 → EDB93D8644 → B9950GC887 → G7410GGDA2 → GFE92E8322 → EDCB0G6544 → GA974CA872 → E8330GEE94 → GBBA0G7662 → GE552ECC32 → ECB76AA654 → A7542EDCA8 → C9731FEA86 → EB630GEB64 → GBA54CC762 → E8752ECA94 → CA730GEA76 → GB632EEB62 → ECB54CC654 → A8774CAA98 → 83320GFEEA → GDBB1F6642 → FD954CC843 → C9870GA986 → G6310GGEB2 → GFEB4C6322 → EDB84C9644 → A9850GC988 → G7210GGFA2 → GFED2E4322 → EDCB886544 → A974HHCA88 → DA420GFD75 → GD982E9842 → EC910GG854 → GFA70GA722 → GED32EE432 → ECBB886654 → A754HHCCA8 → DC53HHDC55 → EC87HH9954 → DC73HHDA55 → EC861FB954 → EA750GCA74 → GA732EEA72 → ECB32EE654 → CBA74CA766 → 86532EECBA → CB751FCA66 → E7652ECBA4 → CA752ECA76 → C7632EEBA6 → CB652ECB66 → C7654CCBA6 → 87652ECBAA → C7531FECA6 → EB762EBA64 → CA552ECC76 → C7762EBAA6 → C6532EECB6 → CB764CBA66 → 86552ECCBA → C7751FCAA6 → E7632EEBA4 → CBA52EC766 → C7652ECBA6C7652ECBA6
1152 max steps800000000DE → ED7HHHHH944 → DDA83HD9745 → E9861HFB984 → GB830HGE962 → HED82HE9431 → GFBA4HC7622 → FEB63HDB633 → ECB74HCA654 → DA763HDBA75 → E8742HEDA94 → FAA61HFB773 → GC942HED852 → FEA83HD9733 → ECB61HFB654 → GB964HCB862 → FC652HECB53 → FC975HBA853 → EA741HFDA74 → GBA62HEB762 → FE853HDC933 → ECB83HD9654 → EA862HEB974 → FA841HFD973 → GCB61HFB652 → GEA64HCB732 → FDA63HDB743 → EC973HDA854 → EA851HFC974 → GB951HFC862 → GEA62HEB732 → FEB83HD9633 → ECB72HEA654 → FA963HDB873 → EC741HFDA54 → GBA84HC9762 → FC641HFDB53 → GCB85HB9652 → FB752HECA63FC963HDB853EC862HEB954FA962HEB873FC841HFD953GCB83HD9652FD862HEB943FCA72HEA753FC952HEC853FC973HDA853EC851HFC954GB973HDA862FD741HFDA43GCB95HB8652FB752HECA63
12102 max steps600000078DDD → DDD875BA9445 → 998630GEB989 → GB510HHGGC62 → HGEBA0G76311 → HFFB52EC6221 → GDDC74CA5442 → E99872EA9884 → CA3110GGGE76 → GFFB62EB6222 → EDDC54CC5444 → A99876AA9888 → 432110GGGFEE → GFFDB9764222 → EDD951FC8444 → EA9970GA8874 → GA3310GGEE72 → GFEBB2E66322 → EDCB54CC6544 → A98774CAA988 → 833210GGFEEA → GFDBB1F66422 → FDD954CC8443 → C99870GA9886 → G63110GGGEB2 → GFFEB4C63222 → EDDB84C96444 → A99850GC9888 → G72110GGGFA2 → GFFED2E43222 → EDDCB8865444 → A9974HHCA888 → DA421HHFFD75 → GFBA62EB7622 → EDC552ECC544 → CA9776AAA876 → 643330GEEEDC → GBBB95B86662 → E65550GCCCB4 → GA7774CAAA72E83332EEEE94CBBBA0G76666G65552ECCCB2EC7774CAAA54A87332EEEA98CBB320GFE666GDB654CCB642E98754CCA984A87310GGEA98GFB320GFE622GEDDB4C64432EB9984C98864A85110GGGC98GFF720GFA222GEDDD2E44432ECB998888654A7510HHGGCA8HGB93HHD8611GGEA51FC7312FFDB72EA6423DDB952EC8645C98750GCA986G76310GGEBA2GFEB52EC6322EDCB74CA6544A98752ECA988C73210GGFEA6GFDB62EB6422EDC954CC8544A98770GAA988G33210GGFEE2GFEDBA664322EDB953DC8644B99750GCA887G74310GGEDA2GFEB92E86322EDCB50GC6544GA9774CAA872E83330GEEE94GBBBA0G76662GE5552ECCC32ECB776AAA654A75432EEDCA8CB9731FEA866EB6530GECB64GBA754CCA762E87532EECA94CBA730GEA766GB6532EECB62ECB754CCA654A87752ECAA98C73320GFEEA6GDBB62EB6642EC9554CCC854A87770GAAA98G33320GFEEE2GEDBBA666432EB9553DCC864B97750GCAA87G74330GEEDA2GEBB92E86632ECB550GCC654GA7774CAAA72
1343 max steps6000000000000 → 5HHHHHHHHHHHC → C4HHHHHHHHHC6 → DB54HHHHHCC65 → DCCB60HGB6555 → HB8764HCBA961 → GD6541HFDCB42 → GEB985HB98632 → FD9530HGEC843 → HDCA83HD97541 → GE9851HFC9832 → GEC940HGD8532 → HEDA83HD97431 → GEB961HFB8632 → GEC852HEC9532 → FEB973HDA8633 → ECB741HFDA654 → GBA863HDB9762 → FD7541HFDCA43 → GCB984HC98652 → FC7630HGEBA53 → HDC963HDB8541 → GE9862HEB9832 → FEB830HGE9633 → HDCB82HE96541 → GFA862HEB9722 → FED841HFD9433 → GCCA94HC87552 → FC7751HFCAA53 → GCA752HECA752 → FE9752HECA833 → FCB951HFC8653 → GCA762HEBA752 → FE9642HEDB833 → FCBA72HEA7653 → FC9642HEDB853 → FCA862HEB9753 → FC9641HFDB853GCB862HEB9652FE9652HECB833FCB962HEB8653FC9652HECB853FC9762HEBA853FC9641HFDB853
1468 max steps1000000008HHHH → HHHH80HHG90001 → HHHHG96A810001 → HHHGF40GD21001 → HHHFFD88422001 → HHGDD8HH844101 → HGGDC54CC54111 → GFF9876AA98222 → EDD4310GGED444 → GFBA9988887622 → ED5310HHGGEC44 → HGDCA90G875411 → HFF9730GEA8221 → HFDDB30GE64421 → HFDB994C886421 → GD98510GGC9842 → GFE9710GGA8322 → GFEDB30GE64322 → GEDBB94C866432 → EB98550GCC9864 → GA77510GGCAA72 → GFE7332EEEA322 → EDCBBB2E666544 → CA97554CCCA876 → 8776330GEEBAAA → GBB5331FEEC662 → FDBB754CCA6643 → C987552ECCA986 → C776310GGEBAA6 → GFB6532EECB622 → EDCB754CCA6544 → A987752ECAA988 → C733210GGFEEA6 → GFDBB62EB66422 → EDC9554CCC8544 → A987770GAAA988 → G333210GGFEEE2 → GFEDBBA6664322 → EDB9553DCC8644 → B997750GCAA887 → G743310GGEEDA2 → GFEBB92E866322 → EDCB550GCC6544 → GA97774CAAA872 → E833330GEEEE94 → GBBBBA0G766662 → GE55552ECCCC32 → ECB7776AAAA654 → A754332EEEDCA8 → CBB9731FEA8666 → EB65530GECCB64 → GBA7754CCAA762 → E875332EEECA94 → CBBA730GEA7666 → GB65532EECCB62 → ECB7754CCAA654 → A877532EECAA98 → CB73320GFEEA66 → GDBB652ECB6642 → EC97554CCCA854 → A877730GEAAA98 → GB33320GFEEE62 → GEDBBB4C666432 → EB98554CCC9864 → A877510GGCAA98GF73320GFEEA22GEDDBB2E664432ECB9954CC88654A877510GGCAA98
1546 max steps10000000001888G → G88810HHHGG9992 → HGF887HHH999211 → GGFA86HHHA97212 → GFFA970HGA87222 → HEED831HFE94331 → GGCBBA4HC766512 → GEC7653HDCBA532 → FDB8763HDBA9643 → EC97541HFDCA854 → GBA8751HFCA9762 → GEA6431HFEDB732 → GECBA73HDA76532 → FDB8642HEDB9643 → FCA9752HECA8753 → FC97531HFECA853 → GCC9751HFCA8552 → GEA7751HFCAA732 → GEC9532HEEC8532 → FEBB973HDA86633 → ECB7541HFDCA654 → GBA8763HDBA9762 → FD75431HFEDCA43 → GCCA984HC987552 → FC77520HGFCAA53 → HECA752HECA7531 → GFB9752HECA8622 → FED9641HFDB8433 → GCCA972HEA87552 → FE97531HFECA833 → GCCB951HFC86552 → GEA7762HEBAA732 → FEB8432HEED9633 → FCBBA72HEA76653 → FC96542HEDCB853 → FCA8762HEBA9753 → FC96431HFEDB853 → GCCA862HEB97552 → FE97641HFDBA833GCCA741HFDA7552GEB8752HECA9632FEB9641HFDB8633GCCA752HECA7552FE97752HECAA833FCB9531HFEC8653GCC9762HEBA8552FE97641HFDBA833
1670 max steps9000000000000999 → 9998HHHHHHHH8889 → 9999888799998889 → 2111110HHGGGGGGG → HGFFFFDHH3222211 → GGFEDDC1F5443212 → FFDDB996A8864423 → DC995410GGDC8855 → GF987710GGAA9822 → GFED3310GGEE4322 → GFEDBBB886664322 → EDB9554HHCCC8644 → DDA87641FDBA9745 → E9985330GEEC9884 → GBBA7110GGGA7662 → GFFE5532EECC3222 → EDDCBB76AA665444 → A9975542EDCCA888 → C9773210GGFEAA86 → GFDB6330GEEB6422 → GEDBB954CC866432 → EB987550GCCA9864 → GA775310GGECAA72 → GFEB7332EEEA6322 → EDCBBB52EC666544 → CA977554CCCAA876 → 87763330GEEEBAAA → GBBB5331FEEC6662 → FDBB7554CCCA6643 → C9877552ECCAA986 → C7763310GGEEBAA6 → GFBB6532EECB6622 → EDCB7554CCCA6544 → A9877752ECAAA988 → C7333210GGFEEEA6 → GFDBBB62EB666422 → EDC95554CCCC8544 → A9877770GAAAA988 → G3333210GGFEEEE2 → GFEDBBBA66664322 → EDB95553DCCC8644 → B9977750GCAAA887 → G7433310GGEEEDA2 → GFEBBB92E8666322 → EDCB5550GCCC6544 → GA977774CAAAA872 → E8333330GEEEEE94 → GBBBBBA0G7666662 → GE555552ECCCCC32 → ECB77776AAAAA654 → A7543332EEEEDCA8 → CBBB9731FEA86666 → EB655530GECCCB64 → GBA77754CCAAA762 → E8753332EEEECA94 → CBBBA730GEA76666 → GB655532EECCCB62 → ECB77754CCAAA654 → A8775332EEECAA98 → CBB73320GFEEA666 → GDBB6552ECCB6642 → EC977554CCCAA854 → A8777330GEEAAA98 → GBB33320GFEEE662 → GEDBBB54CC666432 → EB987554CCCA9864 → A8775310GGECAA98GFB73320GFEEA622GEDDBB52EC664432ECB99754CCA88654A8775310GGECAA98
1749 max steps1000000000001113G → G31110HHHHHGGGGE2 → HGGGFD1HHHF421111 → GGGGFEC1HF5321112 → GFFFEDC8H85432222 → FEDDCA83HD9754433 → ECB99851HFC988654 → GB976310HGGEBA862 → HFED8541HFDC94321 → GGDCA983HD9875412 → GED98520HGFC98432 → HEECA840HGD975331 → HGDBA851HFC976411 → GGFB8641HFDB96212 → GFEDB752HECA64322 → FEDBA863HDB976433 → ECB97541HFDCA8654 → GBA87641HFDBA9762 → GEB75431HFEDCA632 → GECBA863HDB976532 → FDB86541HFDCB9643 → GCB98652HECB98652 → FE976530HGECBA833 → HDCB9641HFDB86541 → GGB98652HECB98612 → GEE96530HGECB8332 → HEDBB962HEB866431 → GFBA7552HECCA7622 → FED97642HEDBA8433 → FCBA9741HFDA87653 → GCB86431HFEDB9652 → GECA8652HECB97532 → FEB97641HFDBA8633 → GCCA7541HFDCA7552 → GEB87752HECAA9632 → FEB96431HFEDB8633 → GCCBA752HECA76552 → FE977642HEDBAA833 → FCBA7431HFEDA7653 → GCCA8642HEDB97552 → FEA87641HFDBA9733 → GCCA7431HFEDA7552GECA8752HECA97532FEB97531HFECA8633GCCB9641HFDB86552GEB87652HECBA9632FEB96541HFDCB8633GCCA8652HECB97552FE977641HFDBAA833GCCA7431HFEDA7552
1869 max steps9000000000DDDDEHHH → HHHEDDDD8844443001 → HHGB9998HH88886101 → HGGB83110GGGE96111 → HFFFFFB50GC6222221 → HFDDDDD74CA4444421 → GD9999982E98888842 → EC9111110GGGGGG854 → GFFFFFA70GA7222222 → GEDDDDD32EE4444432 → ECBB99998888886654 → A7551110HHGGGGCCA8 → HGFFBB53HHDC662211 → GGFECA75HHBA753212 → GFEDA953HHDC874322 → FFDCA8640GDB975423 → GDC997530GECA88542 → GEB977310GGEAA8632 → GFEBB5330GEEC66322 → GEDBBB754CCA666432 → EB9875552ECCCA9864 → CA7775310GGECAAA76 → GFB763332EEEEBA622 → EDCBBB552ECC666544 → CA9777554CCCAAA876 → 877633330GEEEEBAAA → GBBBB5331FEEC66662 → FDBB75554CCCCA6643 → C98777552ECCAAA986 → C77633310GGEEEBAA6 → GFBBB6532EECB66622 → EDCB75554CCCCA6544 → A98777752ECAAAA988 → C73333210GGFEEEEA6 → GFDBBBB62EB6666422 → EDC955554CCCCC8544 → A98777770GAAAAA988 → G33333210GGFEEEEE2 → GFEDBBBBA666664322 → EDB955553DCCCC8644 → B99777750GCAAAA887 → G74333310GGEEEEDA2 → GFEBBBB92E86666322 → EDCB55550GCCCC6544 → GA9777774CAAAAA872 → E83333330GEEEEEE94 → GBBBBBBA0G76666662 → GE5555552ECCCCCC32 → ECB777776AAAAAA654 → A75433332EEEEEDCA8 → CBBBB9731FEA866666 → EB6555530GECCCCB64 → GBA777754CCAAAA762 → E87533332EEEEECA94 → CBBBBA730GEA766666 → GB6555532EECCCCB62 → ECB777754CCAAAA654 → A87753332EEEECAA98 → CBBB73320GFEEA6666 → GDBB65552ECCCB6642 → EC9777554CCCAAA854 → A87773330GEEEAAA98 → GBBB33320GFEEE6662 → GEDBBB554CCC666432 → EB9877554CCCAA9864 → A87753310GGEECAA98GFBB73320GFEEA6622GEDDBB552ECC664432ECB997754CCAA88654A87753310GGEECAA98
1953 max steps1000000000000000001 → 10HHHHHHHHHHHHHHHGH → HG0HHHHHHHHHHHHHG11 → HGG10HHHHHHHHHGG111 → HGGGG1110HGGGG11111 → HGFFFFFFEH222222211 → GGEDDDDDCH444444312 → GEDA99998H888887432 → FDA621110HGGGGFB743 → HFFFECB73HDA6532221 → GFDDCB863HDB9654422 → FEC998652HECB988533 → FCB976310HGGEBA8653 → HFDC96541HFDCB85421 → GGDB98762HEBA986412 → GEEA75420HGFDCA7332 → HEECBA852HEC9765331 → GFBB97641HFDBA86622 → GEDB75541HFDCCA6432 → GECA98763HDBA987532 → FDB864320HGFEDB9643 → HECCA9752HECA875531 → GFB977531HFECAA8622 → GEDC96431HFEDB85432 → GECBA9862HEB9876532 → FEB965420HGFDCB8633 → HECCA8652HECB975531 → GFB977641HFDBAA8622 → GEDB75431HFEDCA6432 → GECBA9863HDB9876532 → FDB865420HGFDCB9643 → HECB98652HECB986531 → GFB976530HGECBA8622 → HEEC96541HFDCB85331 → GGCBA8762HEBA976512 → GEE965431HFEDCB8332 → GECBBA862HEB9766532 → FEB965541HFDCCB8633 → GCCA87652HECBA97552 → FE9776431HFEDBAA833 → GCCBA7431HFEDA76552 → GECA87642HEDBA97532 → FEBA86431HFEDB97633 → GCCBA7541HFDCA76552 → GEB877642HEDBAA9632 → FEBA75431HFEDCA7633 → GCCBA8642HEDB976552 → FEA876541HFDCBA9733 → GCCA86431HFEDB97552 → GECA87641HFDBA97532GECA86431HFEDB97532GECBA8641HFDB976532GECA86541HFDCB97532GECA87641HFDBA97532