Base 18: 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
22 max steps20 → 1G → E3
310 max steps100 → 0HH → GH1 → FH2 → EH3 → DH4 → CH5 → BH6 → AH7 → 9H8 → 8H9
47 max steps2007 → 71FB → E3D4 → B887 → 3HHE → E2E4 → C976 → 61FC
513 max steps70009 → 96HA9 → B0HG7 → H8H81 → G8H82 → F7H93 → E7H94 → D6HA5 → C6HA6 → B5HB7 → C3HD6 → E6HA4 → D7H95 → C5HB6
630 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 → EA2E74
719 max steps1000000 → 0HHHHHH → GHHHHH1 → G0HHHG2 → HF0HG21 → HGDH311 → GGCH412 → GEBH532 → FD8H843 → EB4HC64 → DA5HB75 → C83HD96 → E73HDA4 → EA5HB74 → D93HD85 → E84HC94 → DA3HD75 → E85HB94 → D92HE85 → F94HC83
843 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 → GA74CA72
932 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 → EA73HDA74
1089 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 → C7652ECBA6
1138 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 → FB752HECA63
1246 max steps700000000HHH → HHH6HHHHA001 → HHGB6HHA6101 → HGGBA0G76111 → HFFF52EC2221 → GDDDC6A54442 → E99973DA8884 → B93110GGGE87 → GFFB40GD6222 → GEDD94C84432 → EB9980G98864 → GA5110GGGC72 → GFFE72EA3222 → EDDCB2E65444 → CA9974CA8876 → 863310GGEEBA → GFBB51FC6622 → FDD754CCA443 → C99872EA9886 → C63110GGGEB6 → GFFB64CB6222 → EDD854CC9444 → A99870GA9888 → G32110GGGFE2 → GFFEDA643222 → EDDB93D86444 → B99950GC8887 → G74110GGGDA2 → GFFE92E83222 → EDDCB0G65444 → GA9974CA8872 → E83310GGEE94 → GFBBA0G76622 → GED552ECC432 → ECB976AA8654 → A75430GEDCA8 → GB9731FEA862 → FDB530GEC643 → GCB974CA8652 → E87530GECA94 → GBA730GEA762 → GEB532EEC632 → ECBB74CA6654 → A87552ECCA98 → C77320GFEAA6 → GDB632EEB642 → ECB954CC8654
1337 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 → FC9641HFDB853
1464 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 → A877510GGCAA98
1538 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 → FE97641HFDBA833
1666 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 → A8775310GGECAA98
1741 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 → GCCA7431HFEDA7552
1865 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 → A87753310GGEECAA98
1949 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 → GECA87641HFDBA97532