Base 20: Cycles Sequences: All Cycle Counts

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)		 Frequency Cycle
Length		 Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
23 cycles114×(max) 6 nodes⮎ 0J → I1 → G3 → C7 → 4F → A9 ⮌
57×3 nodes⮎ 2H → E5 → 8B ⮌
19×(fixed) 1 node ⮎ 6D ⮌
31 cycle 1,520×(fixed) (max) 1 node ⮎ 9JA ⮌
42 cycles6,739×(fixed) 1 node ⮎ C3F8 ⮌
2,096×(max) 6 nodes⮎ 52GF → E996 → 7JJC → C6C8 → 63FE → C7B8 ⮌
52 cycles42,066×(max) 4 nodes⮎ D5JD7 → E5JD6 → E7JB6 → D6JC7 ⮌
418×2 nodes⮎ A8JAA → AJJJ9 ⮌
66 cycles92,647×(max) 17 nodes⮎ 840IFC → IB3F82 → GC2G74 → EC4E76 → A84EBA → A2JJGA → H95DA3 → E80IB6 → I82GB2 → GE2G54 → EC8A76 → 851HEC → G93FA4 → DB0I87 → I62GD2 → GE6C54 → C95DA8 ⮌
33,000×5 nodes⮎ 842GFC → EB3F86 → C82GB8 → E42GF6 → EB7B86 ⮌
27,653×6 nodes⮎ A42GFA → EAJJ86 → DB3F87 → C62GD8 → E73FC6 → C84EB8 ⮌
22,986×3 nodes⮎ EC0I76 → I84EB2 → GA2G94 ⮌
684×(fixed) 1 node ⮎ E82GB6 ⮌
110×(fixed) 1 node ⮎ A9JJ9A ⮌
72 cycles488,948×(max) 13 nodes⮎ E84JEB6 → F85JDB5 → EA4JE96 → F84JEB5 → FA5JD95 → EA3JF96 → G94JEA4 → FC4JE75 → FA6JC95 → E92JGA6 → HA4JE93 → GD4JE64 → FC7JB75 ⮌
168,832×(fixed) 1 node ⮎ FA4JE95 ⮌
82 cycles1,155,593×2 nodes⮎ G650IED4 → IC96CA72 ⮌
1,064,462×(max) 11 nodes⮎ 8540IFEC → IB93FA82 → GC30IG74 → IDC4E762 → GA74EC94 → CA50IE98 → I940IFA2 → IGB0I832 → IGD2G632 → GED6C654 → C975DCA8 ⮌
96 cycles5,248,456×(max) 10 nodes⮎ E941JHFA6 → ID94JEA62 → HE83JFB53 → GEA5JD954 → FB93JFA85 → GA71JHC94 → ID92JGA62 → HGA3JF933 → GED5JD654 → FB96JCA85 ⮌
830,652×7 nodes⮎ FA73JFC95 → GA82JGB94 → HC81JHB73 → IEA3JF952 → HFA4JE943 → GDB4JE864 → FC84JEB75 ⮌
327,676×7 nodes⮎ EA62JGD96 → HA83JFB93 → GE71JHC54 → IDB6JC862 → HC73JFC73 → GE84JEB54 → FC95JDA75 ⮌
321,414×2 nodes⮎ GC62JGD74 → HCA5JD973 ⮌
178,572×(fixed) 1 node ⮎ GC83JFB74 ⮌
110×(fixed) 1 node ⮎ AA9JJJ99A ⮌
104 cycles9,449,384×16 nodes⮎ A9542GFEAA → EB90JJIA86 → JDA50IE961 → JH970ICA21 → JHF50IE421 → JHFB8A8421 → IFB31HG842 → HFDB2G8643 → FDB72GC865 → EA752GEC96 → E9850IEBA6 → I9830IGBA2 → IGD30IG632 → IGDD6C6632 → GD775DCC64 → C8754EECB8 ⮌
4,478,763×(max) 23 nodes⮎ 86510IIEDC → IH973FCA22 → GFC50IE744 → ICB94EA872 → GA530IGE94 → IDC90IA762 → IG750IEC32 → IGD94EA632 → GDA70IC964 → IC750IEC72 → IG954EEA32 → GDA90IA964 → IC710IIC72 → IHG54EE322 → GFDA8A9644 → CB720IHC88 → IF542GFE42 → GEBB8A8854 → C9331HGGA8 → GDD40IF664 → ICB76CC872 → G6552GEED4 → EC996CAA76 ⮌
3,432,848×15 nodes⮎ A5410IIFEA → IHB8JJA822 → HHA90IA923 → IFE10II542 → IHGB8A8322 → GFD31HG644 → GDCB6C8764 → C7652GEDC8 → E9753FECA6 → C9850IEBA8 → I9430IGFA2 → IGDB0I8632 → IGD72GC632 → GED74EC654 → CA974ECA98 ⮌
2,668,995×16 nodes⮎ C6532GGED8 → ED973FCA66 → C8750IECB8 → I9542GFEA2 → GEB90IA854 → IC930IGA72 → IGD50IE632 → IGD96CA632 → GD760IDC64 → IC774ECC72 → GA554EEE94 → CA990IAA98 → I4110IIIF2 → IHHGA83222 → GFFD1H6444 → GCBB6C8874 ⮌
112 cycles50,474,532×4 nodes⮎ GC642JGFD74 → HCC95JDA773 → GC652JGED74 → HCB85JDB873 ⮌
4,152,748×(max) 5 nodes⮎ GCA72JGC974 → HC952JGEA73 → HEB72JGC853 → HEB73JFC853 → GEA73JFC954 ⮌
123 cycles115,578,716×16 nodes⮎ C65332GGGED8 → EDD973FCA666 → C87750IECCB8 → I95542GFEEA2 → GEB990IAA854 → IC9310IIGA72 → IHGD50IE6322 → IGFD96CA6432 → GDB760IDC864 → IC7752GECC72 → GE9554EEEA54 → CA9990IAAA98 → I41110IIIIF2 → IHHHGA832222 → GFFFD1H64444 → GCBBB6C88874 ⮌
25,541,679×(max) 28 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 ⮌
110×(fixed) 1 node ⮎ AAA9JJJJ999A ⮌
131 cycle 347,373,580×(max) 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 cycles724,262,181×(max) 40 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 ⮌
87,617,719×12 nodes⮎ CBA7530IGEC988 → ID95430IGFEA62 → IGDB970ICA8632 → IGD7530IGEC632 → IGDD974ECA6632 → GDA7750IECC964 → IC97550IEECA72 → IG99550IEEAA32 → IGD9910IIAA632 → IHGD710IIC6322 → IHGFD74EC64322 → GFDBA74EC98644 ⮌
6,886,454×(fixed) 1 node ⮎ IGD9750IECA632 ⮌
30,058×(fixed) 1 node ⮎ FEA954JJEEA955 ⮌
12,768×(fixed) 1 node ⮎ FFAA54JJEE9945 ⮌
153 cycles1,043,946,360×27 nodes⮎ GED8530JIGEB654 → JFCB984JEBA8741 → IFB7431JHGFC842 → IGECB83JFB87532 → HFDA742JGFC9643 → HECB962JGDA8753 → HEB8641JHFDB853 → IEDA852JGEB9652 → HGB9851JHEBA833 → IEEB631JHGD8552 → IGEB984JEBA8532 → HFC9631JHGDA743 → IEEC962JGDA7552 → HGB9862JGDBA833 → HEDA531JHGE9653 → IEEB983JFBA8552 → HFA9631JHGDA943 → IEEC940JIFA7552 → JGEA972JGCA9531 → IHDB730JIGC8622 → JGGEA63JFD95331 → IGDDA83JFB96632 → HFD9751JHECA643 → IEDA862JGDB9652 → HGB8751JHECB833 → IEEB742JGFC8552 → HGCA973JFCA9733 ⮌
812,021,030×(max) 30 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 ⮌
110×(fixed) 1 node ⮎ AAAA9JJJJJ9999A ⮌
165 cycles1,537,530,896×9 nodes⮎ IGD97510IIECA632 → IHGD9750IECA6322 → IGFD9750IECA6432 → IGDB9750IECA8632 → IGD97530IGECA632 → IGDD9750IECA6632 → IGD97750IECCA632 → IGD97550IEECA632 → IGD99750IECAA632 ⮌
1,455,423,121×(max) 138 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 ⮌
911,820,072×6 nodes⮎ ECB99750IECAA876 → I9855310IIGEEBA2 → IHGD9930IGAA6322 → IGFDD710IIC66432 → IHGDB774ECC86322 → GFDA7552GEEC9644 ⮌
154,652,215×13 nodes⮎ CBA99910IIAAA988 → IH431110IIIIGF22 → IHHHGFDA86432222 → GFFFDB71HC864444 → GCBBB752GEC88874 → EC955332GGGEEA76 → EDD99850IEBAA666 → I9877310IIGCCBA2 → IHGD5530IGEE6322 → IGFDD996CAA66432 → GDB77610IIDCC864 → IHC77552GEECC722 → GFE99554EEEAA544 ⮌
502,626×2 nodes⮎ GFC8843JJFFBB744 → GFCB873JJFCB8744 ⮌
174 cycles5,829,586,692×(max) 31 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 ⮌
2,129,912,522×23 nodes⮎ HEB98641JHFDBA853 → IEDA8531JHGEB9652 → IGEB9851JHEBA8532 → IGEB9631JHGDA8532 → IGEDB851JHEB86532 → IGEB9852JGEBA8532 → HGDB9631JHGDA8633 → IEEDA751JHEC96552 → IGC99862JGDBAA732 → HGDA6420JIHFD9633 → JGEEC973JFCA75531 → IGDA9752JGECA9632 → HGDB8630JIGDB8633 → JFEDA752JGEC96541 → IHCA9862JGDBA9722 → HGFA6420JIHFD9433 → JGEECB93JFA875531 → IGDA9741JHFCA9632 → IGEC9630JIGDA7532 → JGFDB862JGDB86431 → IHDC9752JGECA7622 → HGFB8652JGEDB8433 → HEDCA852JGEB97653 ⮌
503,836,568×9 nodes⮎ GED96420JIHFDA654 → JGDCA873JFCB97631 → IGD96541JHFEDA632 → IGECA873JFCB97532 → HFDA7541JHFEC9643 → IEDBA862JGDB98652 → HGB87531JHGECB833 → IEEDB742JGFC86552 → HGCA9863JFDBA9733 ⮌
134,160,798×7 nodes⮎ HECA8520JIHEB9753 → JGEC9741JHFCA7531 → IIECA752JGEC97512 → IGGB9752JGECA8332 → HGDDB741JHFC86633 → IEEC9763JFDCA7552 → HFA98652JGEDBA943 ⮌
18+---Not showing digit sets 18+ due to verbosity.