Base 19: 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
26 max steps10 → 0I → H1 → F3 → B73FB7
312 max steps100 → 0II → HI1 → GI2 → FI3 → EI4 → DI5 → CI6 → BI7 → AI8 → 9I98IA9I9
413 max stepsA000 → 9II9 → 989A → 1IIH → H0H2HE32FA74B2F8D2F6D6B674DC94DA90HAH0H2
515 max steps10000 → 0IIII → HIII1 → H0IH2 → IEI31 → HEI32 → GDI43 → FBI64 → E8I95 → D5IC6 → D6IB6 → C6IB7 → C4ID7E5IC5D8I96C4ID7
628 max steps4000GG → GG3E23 → EDA755 → 982FAA → D20HG6 → HE6B42 → FA4D84 → B91G98 → F2IIF4 → GDII43 → FE2F44 → DB9876 → 740HEC → HA4D82 → F91G94 → FAII74 → EB4D75 → A83EA9 → B20HG8 → HE2F42 → FD9854 → B80HA8 → H31GF2 → GEB643 → DA4D86 → 971GBA → F40HE4HB9872F40HE4
733 max steps600000E → E5IIIC5 → DD5IC56 → D86IBA6 → C72IFB7 → G84IDA3 → FC4ID64 → EB6IB75 → D83IEA6 → F84IDA4 → EB4ID75 → E95IC95 → D92IF96 → G93IE93 → FD4ID54 → EB7IA75 → D73IEB6 → F85ICA4 → EA3IE85 → F95IC94EA2IF85GA5IC83FB3IE74FB6IB74E93IE95F94ID94EB3IE75F96IB94E91IG95HB4ID72GD5IC53FB7IA74E83IEA5F95IC94
840 max steps10000000 → 0IIIIIII → HIIIIII1 → H0IIIIH2 → IG10HH21 → IGGD4221 → HEE89442 → FAA0H884 → HB21GG72 → GEE3E443 → DBA98876 → 7420HGEC → HEA4D842 → FA91G984 → FB1IIG74 → HE93E942 → FB9II874 → EB71GB75 → F943EE94 → CA9II887 → BA40HE88 → HA31GF82 → GEC1G643 → FDA5C854 → B871GBA8 → F431GFE4 → FCB98764 → B640HEC8 → HA62FC82 → FD61GC54 → FB85CA74 → B741GEB8 → FA42FE84 → DBA1G876 → F741GEB4 → FBA3E874CA41GE87FA51GD84FB81GA74FB41GE74FBA3E874
963 max steps600000899 → 9985ICA9A → D410IHHE6 → IGD7IA521 → HGB5IC722 → GFB4ID733 → FDB5IC754 → EA84IDA85 → E951IGD95 → HB93IE972 → GE71IGB43 → HDC6IB652 → GC75ICB63 → FB64IDC74 → EB74IDB75 → E963IEC95 → F982IFA94 → GB70IHB73 → IE93IE941 → HFA4ID832 → GEB4ID743 → FCA5IC864 → EA63IEC85 → F983IEA94 → FB60IHC74 → ID94ID951 → HE83IEA42 → GEA5IC843 → FC93IE964 → FB82IFA74 → GB82IFA73 → GD82IFA53 → GDA4ID853 → FC84IDA64 → EB73IEB75 → F973IEB94 → FB71IGB74 → HC83IEA62 → GE83IEA43 → FDA5IC854 → EA83IEA85 → F961IGC94 → HC92IF962 → GF92IF933 → GDC5IC653 → FB85ICA74 → EA52IFD85 → GA94ID983 → FC50IHD64 → IDA6IB851 → HD72IFB52 → GFA5IC833 → FDA3IE854 → FB94ID974 → EB61IGC75 → HB84IDA72 → GD62IFC53 → GDA6IB853 → FB72IFB74 → GB83IEA73 → FD72IFB54 → GBA5IC873FB52IFD74GBA5IC873
1037 max steps100000499G → G9940HE993 → HD9IIII852 → GDA93E9853 → DB81IIGA76 → HC950HD962 → HF85IICA32 → GFC71GB633 → FDC63EC654 → CA865CCA87 → 76521GGDCC → FE864DCA44 → BA961GC988 → F631IIGFC4 → HFC92F9632 → FDC5IIC654 → EDA6IIB855 → DD850HDA56 → H8871GBAA2 → GE421GGE43 → FEDA988544 → BA820HGA88 → HE321GGF42 → GEEC986443 → DAA60HC886 → H7621GGCB2 → GEE63EC443 → DBAA5C8876 → 86421GGECB → FEA62FC844 → DBA61GC876 → F7641GECB4 → FBA63EC874CA641GEC87FA651GDC84FB861GCA74FB641GEC74FBA63EC874
1167 max steps9000000BCEE → EECB8I97645 → E9852IFDA95 → GA950IHD983 → IEB50IHD741 → IHD95IC9511 → HHC82IFA612 → HFF93IE9332 → GECC4ID6643 → FCA75ICB864 → EA652IFDC85 → GA973IEB983 → FD730IHFB54 → IEBA5IC8741 → HE952IFD942 → GFB93IE9733 → FDC71IGB654 → HCA74IDB862 → GD752IFDB53 → GDA85ICA853 → FB841IGEA74 → HCB72IFB762 → GF953IED933 → FDC93IE9654 → FB972IFB974 → GB841IGEA73 → HDC72IFB652 → GFA74IDB833 → FDB62IFC754 → GBA74IDB873 → FC642IFEC64 → GBB85ICA773 → FB542IFED74 → GBB95IC9773 → FB541IGED74 → HCB95IC9762 → GC651IGDC63 → HDB75ICB752 → GC853IEDA63 → FD973IEB954 → FB961IGC974 → HC951IGD962 → HFB72IFB732 → GFC83IEA633 → FDC83IEA654 → FB973IEB974 → FB741IGEB74 → HCB73IEB762 → GE853IEDA43 → FDA94ID9854 → EB850IHDA75 → IC962IFC961 → HG962IFC922 → GFE92IF9433 → GDCB4ID7653 → FC874IDBA64 → EB752IFDB75 → GA963IEC983 → FD840IHEA54 → IDB94ID9751 → HE861IGCA42 → HFC83IEA632 → GEC83IEA643FDA83IEA854FB951IGD974HCA61IGC862HFA63IEC832GEC83IEA643
1241 max steps6000000009GI → IG95IIIIC921 → HGD993E99522 → FEB7IIIIA744 → EEBB52FD7745 → DA9843EEA986 → BA721IIGGB88 → HG9830HFA922 → HFEC1IIG6432 → HGEC91G96422 → GEEA5IIC8443 → FEC961GC9644 → FBA65IICC874 → ED9540HED955 → HA987IIAA982 → GB9210HHG973 → HGED3IIE5422 → GGEC90H96423 → HEDA5IIC8542 → GEC951GD9643 → FDA85IICA854 → EDA53IIED855 → FD9952FD9954 → DB87IIIIAA76 → CBBA30HF8777 → HC5441GEED62 → GEAA85CA8843 → DA7221GGGB86 → FEE741GEB444 → FBAAA3E88874 → CA4221GGGE87 → FEEA51GD8444 → FBAA81GA8874 → FB4221GGGE74 → FEEBA3E87444 → CAAA41GE8887 → FA5221GGGD84 → FEEB81GA7444 → FBAA41GE8874FBA421GGE874FEBA41GE8744FBAA41GE8874
1399 max steps9000000009III → III98III99001 → IIHA98I998101 → IHH91IIIG9111 → HHHH87IAA1112 → HGGFA1IG83222 → HFEED6IB54432 → GEBA96IB98743 → FC8430IHFEA64 → IEBB83IEA7741 → HFA742IFEB832 → GFCB72IFB7633 → GDC953IED9653 → FD9872IFBA954 → GBA630IHFC873 → IED952IFD9541 → HGB983IEA9722 → GFD730IHFB533 → IEDCA5IC86541 → HE9863IECA942 → GEA840IHEA843 → IECA61IGC8641 → HHC863IECA612 → HFE863IECA432 → GECA83IEA8643 → FDA841IGEA854 → HCB951IGD9762 → HFB751IGDB732 → HFDA63IEC8532 → GEC973IEB9643 → FDA851IGDA854 → HCA851IGDA862 → HFB741IGEB732 → HFDB73IEB7532 → GEC963IEC9643 → FDA862IFCA854 → GBA741IGEB873 → HDC742IFEB652 → GFB974IDB9733 → FDB641IGEC754 → HCB974IDB9762 → GD7541IGEDB53 → HDC985ICA9652 → GC8640IHECA63 → IEC863IECA641 → HFA863IECA832 → GEC841IGEA643 → HDCA83IEA8652 → GE9741IGEB943 → HDCA71IGB8652 → HFB752IFDB732 → GFCA63IEC8633 → FDC863IECA654 → FB9763IECB974 → FB8541IGEDA74 → HCB962IFC9762 → GF9651IGDC933 → HDDA72IFB8552 → GFA862IFCA833 → GDC941IGE9653 → HDC972IFB9652 → GFA751IGDB833 → HDDA62IFC8552 → GFA873IEBA833 → FDC731IGFB654 → HDBA74IDB8752 → GD8642IFECA53 → GDB973IEB9753 → FD9641IGEC954 → HCB972IFB9762 → GF9541IGED933 → HDDB93IE97552 → GE9861IGCA943 → HDC840IHEA652 → IFD973IEB9531 → HFC961IGC9632 → HFD962IFC9532 → GFCA72IFB8633 → GDC952IFD9653GDA872IFBA853GDA631IGFC853HDDA73IEB8552GE9862IFCA943GDB840IHEA753IEC962IFC9641HGB862IFCA722GFE952IFD9433GDCB93IE97653FD9751IGDB954HCA861IGCA862HFA641IGEC832HFDB83IEA7532GEC962IFC9643GDB862IFCA753GDA752IFDB853GDA862IFCA853GDA741IGEB853HDC962IFC9652GFA762IFCB833GDC952IFD9653
1443 max steps40000000444444 → 4444443EEEEEEF → CAAAAA98888887 → 5222220HGGGGGE → HEEEEE89444442 → FAAAAA0H888884 → HB22221GGGGG72 → GEEEEE3E444443 → DBAAAA98888876 → 7422220HGGGGEC → HEEEEA4D844442 → FAAAA91G988884 → FB2221IIGGGG74 → HGEEC93E964422 → FEBAA5IIC88744 → EEA742IIFEB845 → GEB9760HCB9743 → HDA643IIEEC852 → GFD9851GDA9533 → FDC881IIGAA654 → HEB953IIED9742 → GFD9741GEB9533 → FDCA83IIEA8654 → FEA853IIEDA844 → FEB964IIDC9744 → EEB8631GFCA745 → FCA9641GEC9864 → FBA661IIGCC874 → HEA9540HED9842 → HFAA81IIGA8832 → HGE871IIGBA422 → HGFC960HC96322 → HFEC65IICC6432 → GFDA85IICA8533 → FFBA53IIED8734 → FFBA750HDB8734 → HCB8441GEEA762 → GEAA641GEC8843 → FDAA621GGC8854 → FEB8621GGCA744 → FEBA641GEC8744FBAA641GEC8874FBA6421GGEC874FEBA641GEC8744
15102 max steps40000000059999E → E999953IED99995 → F993IIIIIIIE994 → FE99993IE999944 → FBA4IIIIIIID874 → EEBA874IDBA8745 → EA96431IGFEC985 → HDB9840IHEA9752 → IFD9630IHFC9531 → IHECA72IFB86411 → HHFB852IFDA7312 → HFFCA62IFC86332 → GFCC963IEC96633 → FDC8662IFCCA654 → GBA7663IECCB873 → FD86542IFEDCA54 → GBB9873IEBA9773 → FD74430IHFEEB54 → IEBBA95IC987741 → HE95430IHFED942 → IFEBA93IE987431 → HFCA730IHFB8632 → IFEC952IFD96431 → HGCB972IFB97622 → GFE9541IGED9433 → HDDBA93IE987552 → GE98630IHFCA943 → IEDB840IHEA7541 → IHDA962IFC98511 → HHFA740IHEB8312 → IGFEB72IFB74321 → HGECB73IEB76422 → GFDA853IEDA8533 → FDC9851IGDA9654 → HCA8740IHEBA862 → IFD8531IGFDA531 → HHDCA84IDA86512 → HFD8741IGEBA532 → HFDB962IFC97532 → GFCA751IGDB8633HDDA752IFDB8552GFA8862IFCAA833GDC9421IGGE9653HEDC972IFB96542GFB9751IGDB9733HDDA641IGEC8552HFC9873IEBA9632GEC8530IHFDA643IEDB973IEB97541HFA9641IGEC9832HFDB840IHEA7532IFEB962IFC97431HGCB851IGDA7622HFEB752IFDB7432GFCB963IEC97633FDC8651IGDCA654HCA8763IECBA862GE86531IGFDCA43HDDB973IEB97552GE98641IGECA943HDCA840IHEA8652IFD9741IGEB9531HHDB961IGC97512HGFB751IGDB7322HFEDA63IEC85432GECA973IEB98643FDA8530IHFDA854IEBA851IGDA8741HHC9631IGFC9612HGFD962IFC95322GFECA72IFB86433GDCB852IFDA7653GDA8752IFDBA853GDA8631IGFCA853HDDA741IGEB8552HFC9862IFCA9632GFC9640IHEC9633IEDB862IFCA7541HGB9752IFDB9722GFEA641IGEC8433HDDBA83IEA87552GE98631IGFCA943HDDB840IHEA7552IFD9862IFCA9531HGCA740IHEB8622IFFC852IFDA6331HGCCA73IEB86622GFD8652IFDCA533GDCA873IEBA8653FD97531IGFDB954HDBA861IGCA8752HFB7531IGFDB732HFDCA63IEC86532GEC9763IECB9643FDA8651IGDCA854HCA8741IGEBA862HFC8531IGFDA632HFDCA73IEB86532GEC9752IFDB9643GDB9751IGDB9753HDB8641IGECA752HFC9752IFDB9632GFCA751IGDB8633
1637 max steps2000000000000III → III1IIIIIIIIG001 → IIHH1IIIIIIG1101 → IHHHH210HHG11111 → IGGGGGGD42222221 → HEEEEEE894444442 → FAAAAAA0H8888884 → HB222221GGGGGG72 → GEEEEEE3E4444443 → DBAAAAA988888876 → 74222220HGGGGGEC → HEEEEEA4D8444442 → FAAAAA91G9888884 → FB22221IIGGGGG74 → HGEEEC93E9644422 → FEBAAA5IIC888744 → EEA7431IIGFEB845 → HFCB9760HCB97632 → HFC6643IIEECC632 → GFEB885IICAA7433 → FFCA742IIFEB8634 → GFBB9740HEB97733 → HDCA443IIEEE8652 → GFDA9851GDA98533 → FDC8821IIGGAA654 → HGCB953IIED97622 → GGEB8631GFCA7423 → FEDCA641GEC86544 → FBAA8661GCCA8874 → FB664221GGGECC74 → FEEBA663ECC87444 → CAAA6641GECC8887 → FA665221GGGDCC84 → FEEB8661GCCA7444 → FBAA6641GECC8874FBA66421GGECC874FEBA6641GECC8744FBAA6641GECC8874
17100 max steps20000000000004999 → 99941IIIIIIIGE99A → HE999995IC9999942 → GD92IIIIIIIIIF953 → GFD99531IGFD99533 → HDDCA83IIIEA86552 → GFDC8551IGDDA6533 → HDDA8873IEBAA8552 → GE986321IGGFCA943 → HEDDB840IHEA75542 → IFDA9862IFCA98531 → HGCA7420IHGEB8622 → IFFEC852IFDA64331 → HGCCB973IEB976622 → GFD86541IGEDCA533 → HDDB9873IEBA97552 → GE986430IHFECA943 → IEDBA840IHEA87541 → IHDA9631IGFC98511 → HHGDA740IHEB85212 → IGFFC962IFC963321 → HGECC962IFC966422 → GFEB8662IFCCA7433 → GDCB8652IFDCA7653 → GDA87652IFDCBA853 → GDA87531IGFDBA853 → HDDA8631IGFCA8552 → HFDA8741IGEBA8532 → HFDB9631IGFC97532 → HFDCA751IGDB86532 → HFDA8752IFDBA8532 → GFCA8631IGFCA8633 → HDDC9641IGEC96552 → HFC98762IFCBA9632 → GFC96530IHFDC9633 → IEDCA762IFCB86541 → HGB97652IFDCB9722 → GFEA7541IGEDB8433 → HDDBA962IFC987552 → GFA87530IHFDBA833 → IEDCA631IGFC86541 → HHDB9763IECB97512 → HFE97541IGEDB9432 → HFDBA961IGC987532 → HFDA7530IHFDB8532 → IFECA862IFCA86431 → HGCB8641IGECA7622 → HFEC8652IFDCA6432 → GFCB9763IECB97633 → FDC86541IGEDCA654 → HCB98763IECBA9762 → GE865430IHFEDCA43 → IEDBA973IEB987541 → HFA96430IHFEC9832 → IFECB840IHEA76431 → IHEBA852IFDA87411 → HHFB9631IGFC97312 → HGFDC951IGD965322 → HFEDA872IFBA85432 → GFCB9631IGFC97633 → HDDC9651IGDC96552 → HFB88762IFCBAA732 → GFC95431IGFED9633 → HDDCB972IFB976552 → GFA87541IGEDBA833 → HDDB9631IGFC97552 → HFDA8751IGDBA8532 → HFDA8631IGFCA8532 → HFDCA741IGEB86532 → HFDB9752IFDB97532GFCA8641IGECA8633HDDB8641IGECA7552HFC98752IFDBA9632GFCA7530IHFDB8633IEDCA752IFDB86541HGB98752IFDBA9722GFEA6430IHFEC8433IEDCBA83IEA876541HFA97531IGFDB9832HFDCA630IHFC86532IFECA763IECB86431HFCA8652IFDCA8632GFCA7641IGECB8633HDDB8652IFDCA7552GFA88752IFDBAA833GDCA6321IGGFC8653HEDDA763IECB85542GEA98752IFDBA9843GDB96320IHGFC9753IFDDA751IGDB85531HHDA8862IFCAA8512HFFA7421IGGEB8332HFEDCB72IFB765432GFCB9753IEDB97633FDC97541IGEDB9654HCB98751IGDBA9762HFB75430IHFEDB732IFECB963IEC976431HFCA8651IGDCA8632HFDA7641IGECB8532HFDB9752IFDB97532
1839 max steps300000000000446GGG → GGG6442IIIIFEEC223 → GGGFCCA2IIF8663223 → GGEDD9941GE9955423 → FEDAA87IIIIAA88544 → EEDB764IIIIDCB7545 → EEDD87620HGCBA5545 → HEA988641GECAA9842 → GEAA6221IIGGGC8843 → HGEDCA63IIEC865422 → GGEC98741GEBA96423 → FEDAA641IIGEC88544 → HECB9853IIEDA97642 → GFD986420HGECA9533 → HEDCA861IIGCA86542 → HGDB8743IIEEBA7522 → GGEC97630HFCB96423 → HEDCA663IIECC86542 → GFD987641GECBA9533 → FDCA8641IIGECA8654 → HECA8743IIEEBA8642 → GFDA8742IIFEBA8533 → GFDBA752IIFDB87533 → GFDAA6630HFCC88533 → HDCC86621GGCCA6652 → GEE866661GCCCCA443 → FDAA66661GCCCC8854 → FB8666621GGCCCCA74 → FEB666641GECCCC744 → FBAA66663ECCCC8874 → CA6666421GGECCCC87 → FEA666651GDCCCC844 → FBA866661GCCCCA874 → FB6666421GGECCCC74 → FEBA66663ECCCC8744 → CAA666641GECCCC887 → FA6666521GGDCCCC84 → FEB866661GCCCCA744 → FBA666641GECCCC874FBA666641GECCCC874