Base 20: Cycles Sequences: Maximum Length Cycle Count

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
23 cycles6 nodes⮎ 0J → I1 → G3 → C7 → 4F → A9 ⮌
31 cycle (fixed) 1 node ⮎ 9JA ⮌
42 cycles6 nodes⮎ 52GF → E996 → 7JJC → C6C8 → 63FE → C7B8 ⮌
52 cycles4 nodes⮎ D5JD7 → E5JD6 → E7JB6 → D6JC7 ⮌
66 cycles17 nodes⮎ 840IFC → IB3F82 → GC2G74 → EC4E76 → A84EBA → A2JJGA → H95DA3 → E80IB6 → I82GB2 → GE2G54 → EC8A76 → 851HEC → G93FA4 → DB0I87 → I62GD2 → GE6C54 → C95DA8 ⮌
72 cycles13 nodes⮎ E84JEB6 → F85JDB5 → EA4JE96 → F84JEB5 → FA5JD95 → EA3JF96 → G94JEA4 → FC4JE75 → FA6JC95 → E92JGA6 → HA4JE93 → GD4JE64 → FC7JB75 ⮌
82 cycles11 nodes⮎ 8540IFEC → IB93FA82 → GC30IG74 → IDC4E762 → GA74EC94 → CA50IE98 → I940IFA2 → IGB0I832 → IGD2G632 → GED6C654 → C975DCA8 ⮌
96 cycles10 nodes⮎ E941JHFA6 → ID94JEA62 → HE83JFB53 → GEA5JD954 → FB93JFA85 → GA71JHC94 → ID92JGA62 → HGA3JF933 → GED5JD654 → FB96JCA85 ⮌
104 cycles23 nodes⮎ 86510IIEDC → IH973FCA22 → GFC50IE744 → ICB94EA872 → GA530IGE94 → IDC90IA762 → IG750IEC32 → IGD94EA632 → GDA70IC964 → IC750IEC72 → IG954EEA32 → GDA90IA964 → IC710IIC72 → IHG54EE322 → GFDA8A9644 → CB720IHC88 → IF542GFE42 → GEBB8A8854 → C9331HGGA8 → GDD40IF664 → ICB76CC872 → G6552GEED4 → EC996CAA76 ⮌
112 cycles5 nodes⮎ GCA72JGC974 → HC952JGEA73 → HEB72JGC853 → HEB73JFC853 → GEA73JFC954 ⮌
123 cycles28 nodes⮎ A55430IGFEEA → IDB98JJAA862 → HDA51JJHE963 → IGCB52GE8732 → GED952GEA654 → EC9970ICAA76 → I85510IIEEB2 → IHG992GAA322 → GFED10II6544 → IHCB96CA8722 → GF6530IGED44 → IDCB96CA8762 → G76530IGEDC4 → IDC974ECA762 → GA7550IEEC94 → IC9950IEAA72 → IG9510IIEA32 → IHGD90IA6322 → IGFD70IC6432 → IGDB74EC8632 → GDA752GEC964 → EC9750IECA76 → I98550IEEBA2 → IG9930IGAA32 → IGDD10II6632 → IHGD76CC6322 → GFD764EDC644 → CBA774ECC988 ⮌
131 cycle 52 nodes⮎ GC6530JIGED74 → JFCB85JDB8741 → IFA642JGFD942 → HGCB93JFA8733 → GED841JHFB654 → IDCA84JEB9762 → HE8641JHFDB53 → IEDA84JEB9652 → HE9851JHEBA53 → IEC961JHDA752 → IGC862JGDB732 → HGDA63JFD9633 → GED973JFCA654 → GCA862JGDB974 → HCA641JHFD973 → IED962JGDA652 → HGB873JFCB833 → GED842JGFB654 → HCCA84JEB9773 → GD7541JHFEC64 → IDCA85JDB9762 → HD7641JHFDC63 → IED975JDCA652 → HD9762JGDCA63 → HEA762JGDC953 → HEB862JGDB853 → HEB852JGEB853 → HEB962JGDA853 → HEB851JHEB853 → IEC962JGDA752 → HGB862JGDB833 → HEDA52JGE9653 → HEB983JFBA853 → GEA631JHGD954 → IECB83JFB8752 → HFA742JGFC943 → HECB82JGB8753 → HEB742JGFC853 → HECA73JFC9753 → GEA752JGEC954 → HCB972JGCA873 → HE9541JHFEA53 → IEDA94JEA9652 → HE9840JIFBA53 → JFDA61JHD9641 → IID973JFCA612 → IGF962JGDA432 → HGDC93JFA7633 → GED962JGDA654 → HCB873JFCB873 → GE8542JGFEB54 → HCCA95JDA9773 ⮌
145 cycles40 nodes⮎ A877310IIGCCBA → IHD552JJGEE622 → HHGCB80IB87323 → IFED532GGE6542 → GEDB996CAA8654 → C976310IIGDCA8 → IHD7540IFEC622 → IGFB974ECA8432 → GDBA530IGE9864 → IDC9730IGCA762 → IGD7550IEEC632 → IGD9974ECAA632 → GDA7510IIEC964 → IHC9750IECA722 → IGF9550IEEA432 → IGDB990IAA8632 → IGD7310IIGC632 → IHGDD74EC66322 → GFDA774ECC9644 → CBA7550IEEC988 → I995430IGFEAA2 → IGDB910IIA8632 → IHGD730IGC6322 → IGFDD74EC66432 → GDBA774ECC9864 → CA75530IGEEC98 → ID99540IFEAA62 → IGB9710IICA832 → IHGD530IGE6322 → IGFDD96CA66432 → GDB7760IDCC864 → IC77552GEECC72 → GE99554EEEAA54 → CA99910IIAAA98 → IH41110IIIIF22 → IHHHGFA8432222 → GFFFDB1H864444 → GCBBB72GC88874 → EC55332GGGEE76 → EDD9984EBAA666 ⮌
153 cycles30 nodes⮎ GEA8531JHGEB954 → IECB961JHDA8752 → IGC8641JHFDB732 → IGEC963JFDA7532 → HFDA862JGDB9643 → HEC9751JHECA753 → IEC9752JGECA752 → HGB9752JGECA833 → HEDB741JHFC8653 → IEDA863JFDB9652 → HFA8751JHECB943 → IEDA741JHFC9652 → IGDA862JGDB9632 → HGDA751JHEC9633 → IEEB862JGDB8552 → HGB9852JGEBA833 → HEDB631JHGD8653 → IEEB874JECB8552 → HE99742JGFCAA53 → HECA730JIGC9753 → JFEB752JGEC8541 → IHCA973JFCA9722 → HGE8530JIGEB533 → JFEDB95JDA86541 → IFA9751JHECA942 → IGDA730JIGC9632 → JGFDA62JGD96431 → IHDC973JFCA7622 → HGE9652JGEDA533 → HEDB983JFBA8653 ⮌
165 cycles138 nodes⮎ CA995530IGEEAA98 → ID994110IIIFAA62 → IHHGB710IIC83222 → IHGFFD52GE644322 → GFEDBB96CA886544 → CB976330IGGDCA88 → IDD75430IGFEC662 → IGDB9774ECCA8632 → GDA75530IGEEC964 → IDC99750IECAA762 → IG975510IIEECA32 → IHGD9950IEAA6322 → IGFD9710IICA6432 → IHGDB750IEC86322 → IGFD9752GECA6432 → GEDB9750IECA8654 → IC997530IGECAA72 → IGD95510IIEEA632 → IHGD9970ICAA6322 → IGFD7510IIEC6432 → IHGDB974ECA86322 → GFDA7530IGEC9644 → IDCB9750IECA8762 → IG975530IGEECA32 → IGDD9950IEAA6632 → IGD97710IICCA632 → IHGD7550IEEC6322 → IGFD9974ECAA6432 → GDBA7510IIEC9864 → IHC97530IGECA722 → IGFD9550IEEA6432 → IGDB9970ICAA8632 → IGD75310IIGEC632 → IHGDD974ECA66322 → GFDA7750IECC9644 → ICB97550IEECA872 → IG995530IGEEAA32 → IGDD9910IIAA6632 → IHGD7710IICC6322 → IHGFD754EEC64322 → GFDBA974ECA98644 → CBA75310IIGEC988 → IHD95430IGFEA622 → IGFDB970ICA86432 → IGDB7530IGEC8632 → IGDD9752GECA6632 → GED97750IECCA654 → IC997550IEECAA72 → IG995510IIEEAA32 → IHGD9910IIAA6322 → IHGFD710IIC64322 → IHGFDB74EC864322 → GFDBA752GEC98644 → ECB97530IGECA876 → ID985530IGEEBA62 → IGD99730IGCAA632 → IGDD7510IIEC6632 → IHGD9774ECCA6322 → GFDA7550IEEC9644 → ICB99750IECAA872 → IG955310IIGEEA32 → IHGDD990IAA66322 → IGFD7710IICC6432 → IHGDB754EEC86322 → GFDA9752GECA9644 → ECB97510IIECA876 → IH985530IGEEBA22 → IGFD9930IGAA6432 → IGDDB710IIC86632 → IHGD7752GECC6322 → GFED9754EECA6544 → CBA99750IECAA988 → I9543110IIIGFEA2 → IHHGDB90IA863222 → IGFFD730IGC64432 → IGDDBB74EC886632 → GDA77532GGECC964 → EDC97550IEECA766 → I9987550IEECBAA2 → IG995310IIGEAA32 → IHGDD910IIA66322 → IHGFD770ICC64322 → IGFDB754EEC86432 → GDBA9752GECA9864 → EC975310IIGECA76 → IHD98550IEEBA622 → IGF99730IGCAA432 → IGDDB510IIE86632 → IHGD9772GCCA6322 → GFED7550IEEC6544 → ICB99974ECAAA872 → GA553110IIIGEE94 → IHHDC990IAA76222 → IGFF7510IIEC4432 → IHGDBB94EA886322 → GFDA7330IGGC9644 → IDDCB750IEC87662 → IG977552GEECCA32 → GED99550IEEAA654 → IC999710IICAAA72 → IHG55110IIIEE322 → IHHGFD98AA643222 → GFFDB720IHC86444 → IFCBB752GEC88742 → GEB95532GGEEA854 → EDC99930IGAAA766 → ID875110IIIECB62 → IHHG9752GECA3222 → GFFED950IEA65444 → ICBB9970ICAA8872 → IG553310IIGGEE32 → IHGDDD98AA666322 → GFD77720IHCCC644 → IFCB7554EEEC8742 → GBA99552GEEAA984 → EC993110IIIGAA76 → IHHD8510IIEB6222 → IHGFF972GCA44322 → GFEDBB50IE886544 → ICB99732GGCAA872 → GED55310IIGEE654 → IHDC9996CAAA7622 → GF765110IIIEDC44 → IHHCB974ECA87222 → GFFA5530IGEE9444 → IDCBB990IAA88762 → IG753310IIGGEC32 → IHGDDD94EA666322 → GFDA7770ICCC9644 → ICB75550IEEEC872 → IG999552GEEAAA32 → GED99110IIIAA654 → IHHC9710IICA7222 → IHGFF550IEE44322 → IGFDBB98AA886432 → GDB73320IHGGC864 → IFDDC752GEC76642 → GEB97754EECCA854 ⮌
174 cycles31 nodes⮎ HEDA6431JHGFD9653 → IEECA873JFCB97552 → HFA97541JHFECA943 → IEDBA730JIGC98652 → JGFB8641JHFDB8431 → IIECB952JGEA87512 → IGGB9741JHFCA8332 → IGEDC841JHFB76532 → IGECA863JFDB97532 → HFDA8641JHFDB9643 → IEDB9751JHECA8652 → IGC98641JHFDBA732 → IGEC9641JHFDA7532 → IGECA862JGDB97532 → HGDB8641JHFDB8633 → IEEC9752JGECA7552 → HGB99752JGECAA833 → HEDB7420JIHFC8653 → JGEDA863JFDB96531 → IGDA8751JHECB9632 → IGEB8641JHFDB8532 → IGECA852JGEB97532 → HGDB9741JHFCA8633 → IEEC9641JHFDA7552 → IGDA9862JGDBA9632 → HGDA7520JIHEC9633 → JGEEB862JGDB85531 → IHDB9852JGEBA8622 → HGFB8531JHGEB8433 → IEEDCA62JGD976552 → HGB98762JGDCBA833 ⮌