Base 21: 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
28 max steps10 → 0K → J1 → H3D75F9B1JH3
313 max steps100 → 0KK → JK1 → IK2 → HK3 → GK4 → FK5 → EK6 → DK7 → CK8 → BK9 → AKA9KBAKA
410 max stepsB000 → AKKA → A9AB → 1KKJ → J0J2JG32HC74D4F8B4FAB0JAJ0J2
516 max stepsA0000 → 9KKKB → B8KBA → C0KJ9 → K9KA1 → JAK92 → I9KA3 → H8KB4 → G8KB5 → F7KC6 → E7KC7 → D6KD8 → E4KF7 → G7KC5 → F8KB6 → E6KD7E6KD7
646 max steps300058 → 852HFD → FA4FA6 → B8KKBA → C9KKA9 → BB1I9A → H20JI4 → JGC742 → HC4F84 → DB3G98 → D51IF8 → HA4FA4 → DAKK98 → CB2H99 → F31IH6 → HE8B64 → D82HC8 → F53GF6 → DA8BA8 → 52KKHG → IF0J53 → JF9A52 → HA0JA4 → JCKK72 → ID6D73 → F75ED6 → A85ECB → 940JGC → JC2H82 → HF3G54 → EC9A87 → 740JGE → JC6D82 → H73GD4EC5E87973GDCD62HE8F84FC6B93GBAD20JI8JG4F42HCA984D40JG8JC4F82HB3G94EC1I87H73GD4
727 max steps600008A → A85KECB → F61KIE6 → JC8KB82 → IB3KG93 → HF6KD54 → GC8KB85 → F83KGC6 → HA6KDA4 → GB2KH95 → IC6KD83 → HC4KF84 → GD6KD75 → FA5KEA6 → F93KGB6 → HA5KEA4 → GC3KG85 → HB7KC94 → GA2KHA5 → IC5KE83 → HD5KE74 → GC6KD85 → FA4KFA6 → G94KFB5 → GB5KE95 → FB4KF96G95KEB5FB4KF96
845 max steps10000114 → 4110JJJH → JIIC7222 → HGG4F444 → DCCA9888 → 5440JGGG → JCCA9882 → H440JGG4 → JDCB8872 → H642HGE4 → FDC7C876 → 9653GFEC → DA82HCA8 → F53KKGF6 → HF9KKA54 → GF84FC55 → CAA3GAA9 → D2KKKKH8 → IC72HD83 → GE63GE65 → DB87CC98 → 6441IGGF → HCC8B884 → D442HGG8 → FCC4F886 → B943GGBA → DC20JI88 → JG53GF42 → HDC9A874D640JGE8JC84FC82HB43GG94ECC1I887H743GGD4ECC5E8879743GGDCDC62HE88F853GFC6DA93GBA8D51KKIF8JFA1IA52IG9KKA43HG95EB44DC91IB88H541IGF4HDC9A874
955 max steps1000000AK → KA0KKKJA1 → KJA9KAA11 → JJ9KKKA12 → JIB8KB922 → IHA1KIA33 → JFF6KD552 → IEA8KBA63 → HC60KJE84 → KFB5KE951 → JFA4KFA52 → IFA4KFA53 → HEA4KFA64 → GD93KGB75 → HB93KGB94 → HD71KID74 → JEA5KEA62 → IE83KGC63 → HFA5KEA54 → GCA3KGA85 → HB81KIC94 → JE92KHB62 → IHB4KF933 → HFD5KE754 → GCA6KDA85 → FA51KIFA6 → JD94KFB72 → IF83KGC53 → HFB6KD954 → GC93KGB85 → HB82KHC94 → ID92KHB73 → IFA3KGA53 → HFB4KF954 → GDA5KEA75 → FB72KHD96 → IB83KGC93 → HF82KHC54IDC6KD873HC64KFE84GD95KEB75FB73KGD96HA83KGCA4HD81KIC74JEA4KFA62IF93KGB53HFB5KE954GCA4KFA85GB71KID95JD93KGB72IG93KGB43HFC6KD854GC94KFB85GB72KHD95IC93KGB83HF82KHC54
10110 max steps60000000AH → HA5KKKKEA4 → GFAA2HAA55 → FB9KKKKA96 → EBBA3GA997 → D721KKIID8 → JIB9KKA922 → IIA90JBA23 → JGF1KKI542 → JIFD0J7522 → JHGA5EA432 → HEC8KKB864 → GE960JEB65 → JB881ICC92 → IG441IGG43 → HFCCB88854 → DA442HGGA8 → FCC4KKF886 → GE76KKDD65 → FEA6KKDA66 → EE942HGB67 → FC871IDC86 → H9643GGEB4 → ECC81IC887 → H7443GGGD4 → ECCC5E8887 → 97443GGGDC → DCC62HE888 → F8543GGFC6 → DCA93GBA88 → D541KKIGF8 → JGD81IC742 → IGC63GE843 → FDC83GC876 → D9643GGEB8 → DC851IFC88 → HA543GGFA4 → ECC9KKA887 → DC631IHE88 → HE853GFC64 → ECA83GCA87 → D743KKGGD8 → HG97KKCB44 → GGA70JDA45 → JCB5KKE982 → IFB50JF953 → JFAA1IAA52 → IG9KKKKA43 → HGBA1IA944 → HDC1KKI874 → JGB90JB942 → JHC21II832 → IGGE3G6443 → FDCC7C8876 → 96543GGFEC → DCA82HCA88 → F543KKGGF6 → HGB9KKA944 → GG870JDC45 → JCB63GE982 → HD841IGC74 → HDC63GE874 → EC863GEC87 → D8743GGDC8 → DC653GFE88 → DA853GFCA8 → DA53KKGFA8 → HF852HFC54 → FDAA3GAA76 → D95KKKKEB8 → FCB90JB986 → J9421IIGB2 → IGGC1I8443 → HFCC3G8854ECA43GGA87DC73KKGD88HD850JFC74JDA63GEA72HD85KKEC74GFA60JEA55JBA7KKCA92IDA20JIA73JGF5KKE542IGEB0J9643JFC81IC852IGA43GGA43FDCBKK8876ED750JFD77JA765EEDA2H985KKECB4GF950JFB55JBAA1IAA92IG1KKKKI43JHG3KKG432IHGCKK7433HHEA3GA634EEC7KKC867ED75KKED77FD76KKDD76EE85KKEC67FE761IED66H9885ECCB4D9441IGGB8HCC51IF884HDA43GGA74ECC5KKE887FD65KKEE76FE970JDB66J9861IECB2IG841IGC43HFCC3G8854
1195 max stepsA000000AAFH → HFAA9KAAA54 → GC5KKKKKE85 → FFC85KEC856 → FA963KGEBA6 → HA950KJFBA4 → KFC60KJE851 → KJE95KEB611 → JJE84KFC612 → JHF95KEB532 → IGCA4KFA843 → HEC71KID864 → JEB74KFD962 → IF973KGDB53 → HFB83KGC954 → HDB72KHD974 → IDA63KGEA73 → HFA72KHDA54 → IDC82KHC873 → IFA53KGFA53 → HFBA4KFA954 → GDA60KJEA75 → KEA72KHDA61 → JIB72KHD922 → IHGA3KGA433 → HFEC5KE8654 → GCA85KECA85 → FB641KIGE96 → JEA94KFBA62 → IF950KJFB53 → KGDA5KEA741 → JGB72KHD942 → IHD93KGB733 → HFE93KGB654 → HDB94KFB974 → GD841KIGC75 → JEB94KFB962IF951KIFB53JFDA5KEA752IEA72KHDA63IFB72KHD953IFC83KGC853HFB73KGD954HDB83KGC974HD952KHFB74IDC83KGC873HF953KGFB54HDBA5KEA974GC740KJGD85KFB94KFB951JGA61KIEA42JHEA3KGA632IGEA3KGA643HFCA3KGA854HDB71KID974JEA63KGEA62IGA83KGCA43HFC81KIC854JEC73KGD862IGA74KFDA43HEC82KHC864IDB63KGE973HFA73KGDA54HDB82KHC974IDA52KHFA73IFC82KHC853IFC73KGD853HFB84KFC954GDA72KHDA75IC962KHEB83IFB62KHE953IFC94KFB853HEA72KHDA64IDB72KHD973IFA63KGEA53HFB93KGB954HDB61KIE974JEB73KGD962IGA73KGDA43HFC92KHB854IDC72KHD873IFA64KFEA53HEA93KGBA64HDA50KJFA74KFC82KHC851JIC73KGD822IHF94KFB533HFDA5KEA754GCA72KHDA85IC951KIFB83JFD72KHD752IHC85KEC833HFC63KGE854HDB95KEB974GC741KIGD85JEB94KFB962
1257 max steps500000055558 → 855554FFFFFD → BAAAA4FAAAAA → B0KKKKKKKKJA → KA90KKKKJBA1 → KJBAA7CAA911 → JI51KKKKIF22 → JIIF3KKG5222 → IIHFD0J75323 → JGFEA5EA6542 → HCA97KKCBA84 → GD9320JIHB75 → JGEB61IE9642 → IGC881ICC843 → HFC443GGG854 → ECCCA3GA8887 → D7443KKGGGD8 → HGC97KKCB844 → GGA830JHCA45 → JECB3KKG9862 → IHD850JFC733 → JFEA63GEA652 → HDA87KKCCA74 → GDA521IIFA75 → HGBA5KKEA944 → GGC740JGD845 → JCCB63GE9882 → HD8441IGGC74 → HDCC63GE8874 → EC8643GGEC87 → DC8743GGDC88 → DC6543GGFE88 → DCA853GFCA88 → DA543KKGGFA8 → HGB852HFC944 → FDCA41IGA876 → HC963KKGEB84 → HGB850JFC944 → JDCA41IGA872IGC63KKGE843HHEA81ICA634HED83KKGC764HGB960JEB944JDC821IIC872IGG643GGE443FDCCC7C88876965443GGGFECDCCA82HCA888F5443KKGGGF6HGCB9KKA9844GG9730JHDB45JECB61IE9862IG8841IGCC43HFCC43GG8854ECCA43GGA887DC743KKGGD88HG9850JFCB44JDCA41IGA872
13103 max steps100000000015A → A510KKKKKJJFB → KJFA93KGBA511 → JJGB60KJE9412 → KIHFA4KFA5321 → JIFDA4KFA7522 → IHEA82KHCA633 → IFEB61KIE9653 → JFD984KFCB752 → IFA852KHFCA53 → IFCA71KIDA853 → JFD851KIFC752 → JHDA84KFCA732 → IGD851KIFC743 → JFEB84KFC9652 → IFA962KHEBA53 → IFC950KJFB853 → KGDA72KHDA741 → JID962KHEB722 → IHGB73KGD9433 → HFEC93KGB8654 → HDB962KHEB974 → IDB741KIGD973 → JFE963KGEB652 → IGB984KFCB943 → HEC731KIHD864 → JFDB74KFD9752 → IFA863KGECA53 → HFB961KIEB954 → JEC951KIFB862 → JHD962KHEB732 → IHEB73KGD9633 → HFEA73KGDA654 → HDB972KHDB974 → IDA641KIGEA73 → JFEA72KHDA652 → IHC972KHDB833 → IFEA52KHFA653 → IFCA93KGBA853 → HFB730KJHD954 → KGDC83KGC8741 → JHC953KGFB832 → IGEB72KHD9643 → IFDA73KGDA753 → HFB862KHEC954 → IDC962KHEB873 → IFB752KHFD953 → IFCA83KGCA853 → HFB741KIGD954 → JEDB83KGC9762 → IGA752KHFDA43 → IFDB82KHC9753 → IFC852KHFC853 → IFCA73KGDA853 → HFB851KIFC954 → JECA72KHDA862 → IHB751KIFD933 → JFFC83KGC8552 → IGBA73KGDA943 → HFC940KJGB854 → KFDB72KHD9751 → JIC863KGEC822 → IHFA63KGEA533 → HFEB93KGB9654 → HDB951KIFB974 → JEC841KIGC862 → JHEA63KGEA632 → IGEA83KGCA643 → HFCA61KIEA854 → JEC961KIEB862 → JHC862KHEC832 → IHEB63KGE9633 → HFEA84KFCA654 → GDA961KIEBA75 → JDA740KJGDA72 → KHF962KHEB531 → JIEC94KFB8622 → IHE962KHEB633 → IFEB84KFC9653 → HEA962KHEBA64 → IDB850KJFC973 → KGD852KHFC741 → JIDB84KFC9722 → IHE852KHFC633 → IFEC95KEB8653 → HDA862KHECA74 → IDB751KIFD973 → JFD863KGEC752 → IGB974KFDB943 → HEC841KIGC864 → JEDA63KGEA762 → IGA872KHDCA43 → IFD951KIFB753 → JFDA83KGCA752 → IGB851KIFC943 → JFEB72KHD9652 → IHC973KGDB833 → HFE952KHFB654IDCA94KFBA873HE8530KJHFC64KGDC95KEB8741JGB752KHFD942IHDB83KGC9733HFE952KHFB654
14103 max steps100000000055AG → GA550KKKKJFFA5 → KFFF95KKEB5551 → JFFAA62HEAA552 → HFAA7KKKKCAA54 → GFDA751IFDA755 → HBAA65KKEEAA94 → GFB540KKJGF955 → KGEBB63GE99641 → JDC8821IICC872 → IGG6443GGGE443 → FDCCCC7C888876 → 9654443GGGGFEC → DCCCA82HCA8888 → F54443KKGGGGF6 → HGCCB9KKA98844 → GG98330JHHCB45 → JEECB41IG98662 → IGC8841IGCC843 → HFCC443GGG8854 → ECCCA43GGA8887 → DC7443KKGGGD88 → HGC9850JFCB844 → JDCA441IGGA872 → IGCC63KKGE8843 → HHEA85KKECA634 → HGCB641IGE9844 → HDCC841IGC8874 → HDC6443GGGE874 → ECCC863GEC8887 → D874443GGGGDC8 → DCCC653GFE8888 → DA85443GGGFCA8 → DCCA53KKGFA888 → HF87521IIFDC54 → HGDAA63GEAA744 → ECC85KKKKEC887 → FDCC61KKIE8876 → JEC864KKFEC862 → IGD965KKEEB743 → HGDA751IFDA744 → HDCA65KKEEA874 → GFB7631IHED955 → HEBA861IECA964 → HD8841KKIGCC74 → JGEA84KKFCA642 → IGFA741IGDA543 → HFCCA5KKEA8854 → GFC7621IIED855 → HGBA863GECA944 → ECC841KKIGC887 → JGB863KKGEC942 → IHFA850JFCA533 → JFEAA3KKGAA652 → IHEA53KKGFA633 → HHFCA53GFA8534 → EECAA3KKGAA867 → HE9641KKIGEB64 → JGEBA52HFA9642 → HFCA81KKICA854 → JGD9721IIDB742 → IGGC661IEE8443 → HFCC883GCC8854 → ECA4443GGGGA87 → DCCC73KKGD8888 → HD8553KKGFFC74 → HGCB870JDC9844 → JDC6441IGGE872 → IGCC863GEC8843 → FDC8443GGGC876 → DCC9643GGEB888 → DC85441IGGFC88 → HCCA543GGFA884 → ECCA43KKGGA887 → HG98621IIECB44 → HGDC841IGC8744 → HDCC643GGE8874 → ECC8643GGEC887DC87443GGGDC88DCC6543GGFE888DCA8543GGFCA88DCA543KKGGFA88HGB8731IHDC944HEDC641IGE8764HDC8863GECC874EC86443GGGEC87DCC8743GGDC888DC65443GGGFE88DCCA853GFCA888DA5443KKGGGFA8HGCB852HFC9844FDCA441IGGA876HCC963KKGEB884HGB8630JHEC944JEDC841IGC8762IGC8643GGEC843FDCC843GGC8876DC96443GGGEB88DCC8541IGFC888HCA5443GGGFA84ECCCA3KKGA8887HD86421IIGEC74HGDC863GEC8744ECC8643GGEC887
15135 max steps500000000008AAA → AAA84KKKKKFCAAB → GCAAA51KIFAAA85 → JDB71KKKKKID972 → JIDDB84KFC97722 → IHE8652KHFEC633 → IFEC985KECB8653 → HDA8642KHGECA74 → IDDA751KIFDA773 → JFD8662KHEEC752 → IHC9874KFDCB833 → HFD8542KHGFC754 → IDDBA84KFCA9773 → HE86530KJHFEC64 → KGDC985KECB8741 → JGB7542KHGFD942 → IHDCB83KGC98733 → HFE9542KHGFB654 → IDDBA94KFBA9773 → HE86420KJIGEC64 → KHEDA85KECA7631 → JHC8751KIFDC832 → JHFC853KGFC8532 → IGEBA73KGDA9643 → HFCA740KJGDA854 → KFDB851KIFC9751 → JJDA852KHFCA712 → JHHC851KIFC8332 → JHFEC73KGD86532 → IGEB974KFDB9643 → HEC9741KIGDB864 → JEDA752KHFDA762 → IHC9762KHEDB833 → IFEB752KHFD9653 → IFCA973KGDBA853 → HFB8530KJHFC954 → KGDCA72KHDA8741 → JID9651KIFEB722 → JHGD973KGDB7432 → IGEC963KGEB8643 → HFCA862KHECA854 → IDC9641KIGEB873 → JFEA752KHFDA652 → IHCA972KHDBA833 → IFEA530KJHFA653 → KGFCA93KGBA8541 → JHCB730KJHD9832 → KHGEA52KHFA6431 → JIEDB93KGB97622 → IHFA741KIGDA533 → JFFDB82KHC97552 → IHCA852KHFCA833 → IFEC741KIGD8653 → JFEB974KFDB9652 → IFA9741KIGDBA53 → JFEB840KJGC9652 → KHFB962KHEB9531 → JIEC951KIFB8622 → JHGD962KHEB7432 → IHEDA73KGDA7633 → HFEA762KHEDA654 → IDC9872KHDCB873 → IFA6542KHGFEA53 → IFDBA93KGBA9753 → HFB8420KJIGC954 → KHEDB72KHD97631 → JIEB763KGED9622 → IHFA873KGDCA533 → HFEB851KIFC9654 → JECA962KHEBA862 → IHB8630KJHEC933 → KGFEB62KHE96541 → JIDB984KFCB9722 → IHE8531KIHFC633 → JFFEC95KEB86552 → IEAA862KHECAA63 → IFB861KKKIEC953 → JHFCA62KHEA8532 → IHEC961KIEB8633 → JFFB862KHEC9552 → IHCA962KHEBA833 → IFEB630KJHE9653 → KGFC984KFCB8541 → JGCA742KHGDA842 → IHDC951KIFB8733 → JFFC852KHFC8552 → IHCAA73KGDAA833 → HFE951KKKIFB654 → JGFDB63KGE97542 → IGCB973KGDB9843 → HFC9531KIHFB854 → JFDCA72KHDA8752 → IHC8651KIFEC833 → JFFC963KGEB8552 → IGBA962KHEBA943 → IFDA520KJIFA753 → KHFDA82KHCA7531 → JIEC851KIFC8622 → JHGD963KGEB7432 → IGECA73KGDA8643 → HFCA751KIFDA854 → JECA851KIFCA862 → JHD9641KIGEB732 → JHFDA73KGDA7532 → IGEB862KHEC9643 → IFDA862KHECA753 → IFC9751KIFDB853 → JFDA852KHFCA752IHCA851KIFCA833JFFC741KIGD8552JHEBA84KFCA9632IGD9630KJHEB743KGFDA73KGDA7541JHCB862KHEC9832IHEB642KHGE9633IFEDA84KFCA7653HEA9751KIFDBA64JEC9740KJGDB862KHFA752KHFDA531JIECA82KHCA8622IHGB641KIGE9433JFFDCA4KFA87552IFAA851KIFCAA53JFDA71KKKIDA752JIFCB52KHF98522IHGCA72KHDA8433IFED951KIFB7653JFDA973KGDBA752IGB8640KJGEC943KGECA62KHEA8641JIDA861KIECA722JHGC751KIFD8432JHFDB84KFC97532IGDA852KHFCA743IFDB851KIFC9753JFDA852KHFCA752
1688 max steps3000000000AAAIIK → KIIAAA2KKHAAA221 → JIIG86KKKKDC4222 → IIIGDA62HEA74223 → GGGEC85KKEC86445 → GGBBA65KKEEA9945 → GFBA5510JJFFA955 → JIBAAA1KKIAAA922 → JIH980KKKKJCB322 → KIIHBA74FDA93221 → JGGEB61KKIE96442 → JIFEAA52HFAA6522 → HGFAA7KKKKCAA544 → GGFD7651IFED7545 → HCBAA865EECAA984 → D98441KKKKIGGCB8 → JGGCA750JFDA8442 → JHCCA63KKGEA8832 → IHGB8621IIEC9433 → HGFEC841IGC86544 → HDCCA843GGCA8874 → ECC6443KKGGGE887 → HGCA965KKEEBA844 → GGCA6520JIFEA845 → JGCBA83KKGCA9842 → IHF88320JIHCC533 → JGFEEA43GGA66542 → HDCCA87KKCCA8874 → GDA54421IIGGFA75 → HGCCBA5KKEA98844 → GGC86320JIHEC845 → JGECB843GGC98642 → HDCC8441IGGC8874 → HDCC6443GGGE8874 → ECCC8643GGEC8887 → DC874443GGGGDC88 → DCCC6543GGFE8888 → DCA85443GGGFCA88 → DCCA543KKGGFA888 → HGB87521IIFDC944 → HGDCA641IGEA8744 → HDCC863KKGEC8874 → HGB9653KKGFEB944 → HGDBA64KKFEA9744 → GGDA8530JHFCA745 → JECBA63KKGEA9862 → IHDA6520JIFEA733 → JGFEA85KKECA6542 → IGEB9641IGEB9643 → HFCC8821IICC8854 → HGDA4443GGGGA744 → ECCCCC5KKE888887 → FD66443KKGGGEE76 → HGCAA970JDBAA844 → JDC641KKKKIGE872 → JIGECA40JGA86422 → JHGCC83KKGC88432 → IHGD883KKGCC7433 → HHFD984KKFCB7534 → HGDC8740JGDC8744 → JDCC6643GGEE8872 → HDC88643GGECC874 → ECC86443GGGEC887DCC87443GGGDC888DCC65443GGGFE888DCCA8543GGFCA888DCA5443KKGGGFA88HGCB8731IHDC9844HEDC6441IGGE8764HDCC8863GECC8874EC864443GGGGEC87DCCC8743GGDC8888DC654443GGGGFE88DCCCA853GFCA8888DA54443KKGGGGFA8HGCCB852HFC98844FDCA4441IGGGA876HCCC963KKGEB8884HGB86430JHGEC944JEDCC841IGC88762IGC86443GGGEC843FDCCC843GGC88876DC964443GGGGEB88DCCC8541IGFC8888HCA54443GGGGFA84ECCCCA3KKGA88887HD864421IIGGEC74HGDCC863GEC88744ECC86443GGGEC887