Base 21: 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
23 max steps10 → 0K → J1 → H3
311 max steps100 → 0KK → JK1 → IK2 → HK3 → GK4 → FK5 → EK6 → DK7 → CK8 → BK9 → AKA
44 max stepsB000 → AKKA → A9AB → 1KKJ → J0J2
515 max stepsA0000 → 9KKKB → B8KBA → C0KJ9 → K9KA1 → JAK92 → I9KA3 → H8KB4 → G8KB5 → F7KC6 → E7KC7 → D6KD8 → E4KF7 → G7KC5 → F8KB6 → E6KD7
633 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 → H73GD4
725 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 → FB4KF96
830 max steps200000AK → KA1KKIA1 → JJA7CA12 → IH4KKF33 → HHE1I634 → HED7C764 → D864FEC8 → B853GFCA → DA40JGA8 → JC4KKF82 → IGB2H943 → GEC1I865 → HB83GC94 → EC41IG87 → HC73GD84 → EC63GE87 → D873GDC8 → D653GFE8 → DA84FCA8 → B53KKGFA → HF63GE54 → ECA7CA87 → 753KKGFE → HF90JB54 → JDA1IA72 → IG5KKE43 → HGD1I744 → HDC5E874 → D963GEB8 → D851IFC8 → HA53GFA4
937 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 → HF82KHC54
1073 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 → HFCC3G8854
1136 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 → JEB94KFB962
1238 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 → JDCA41IGA872
1397 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 → HFE952KHFB654
1477 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 → ECC8643GGEC887
15107 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 → JFDA852KHFCA752
1662 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 → ECC86443GGGEC887