Base 19: 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
24 max steps10 → 0I → H1 → F3 → B7
310 max steps100 → 0II → HI1 → GI2 → FI3 → EI4 → DI5 → CI6 → BI7 → AI8 → 9I9
44 max stepsA000 → 9II9 → 989A → 1IIH → H0H2
512 max steps10000 → 0IIII → HIII1 → H0IH2 → IEI31 → HEI32 → GDI43 → FBI64 → E8I95 → D5IC6 → D6IB6 → C6IB7 → C4ID7
626 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 → F40HE4
719 max steps600000E → E5IIIC5 → DD5IC56 → D86IBA6 → C72IFB7 → G84IDA3 → FC4ID64 → EB6IB75 → D83IEA6 → F84IDA4 → EB4ID75 → E95IC95 → D92IF96 → G93IE93 → FD4ID54 → EB7IA75 → D73IEB6 → F85ICA4 → EA3IE85 → F95IC94
835 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 → FBA3E874
961 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 → GBA5IC873
1032 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 → FBA63EC874
1162 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 → GEC83IEA643
1238 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 → FBAA41GE8874
1378 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 → GDC952IFD9653
1440 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 → FEBA641GEC8744
1539 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 → GFCA751IGDB8633
1634 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 → FBAA6641GECC8874
1769 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 → HFDB9752IFDB97532
1838 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 → FBA666641GECCCC874