Base 21: 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--
21 cycle 5 nodes⮎ 1J → H3 → D7 → 5F → 9B ⮌
31 cycle 2 nodes⮎ 9KB → AKA ⮌
49 cycles6 nodes⮎ 50JG → JA92 → H0J4 → JC72 → H4F4 → DA98 ⮌
51 cycle (fixed) 1 node ⮎ E6KD7 ⮌
61 cycle 13 nodes⮎ 973GDC → D62HE8 → F84FC6 → B93GBA → D20JI8 → JG4F42 → HCA984 → D40JG8 → JC4F82 → HB3G94 → EC1I87 → H73GD4 → EC5E87 ⮌
73 cycles4 nodes⮎ E93KGB7 → H94KFB4 → GD5KE75 → FB6KD96 ⮌
84 cycles17 nodes⮎ 9743GGDC → DC62HE88 → F853GFC6 → DA93GBA8 → D51KKIF8 → JFA1IA52 → IG9KKA43 → HG95EB44 → DC91IB88 → H541IGF4 → HDC9A874 → D640JGE8 → JC84FC82 → HB43GG94 → ECC1I887 → H743GGD4 → ECC5E887 ⮌
94 cycles18 nodes⮎ FB73KGD96 → HA83KGCA4 → HD81KIC74 → JEA4KFA62 → IF93KGB53 → HFB5KE954 → GCA4KFA85 → GB71KID95 → JD93KGB72 → IG93KGB43 → HFC6KD854 → GC94KFB85 → GB72KHD95 → IC93KGB83 → HF82KHC54 → IDC6KD873 → HC64KFE84 → GD95KEB75 ⮌
102 cycles37 nodes⮎ D9441IGGB8 → HCC51IF884 → HDA43GGA74 → ECC5KKE887 → FD65KKEE76 → FE970JDB66 → J9861IECB2 → IG841IGC43 → HFCC3G8854 → ECA43GGA87 → DC73KKGD88 → HD850JFC74 → JDA63GEA72 → HD85KKEC74 → GFA60JEA55 → JBA7KKCA92 → IDA20JIA73 → JGF5KKE542 → IGEB0J9643 → JFC81IC852 → IGA43GGA43 → FDCBKK8876 → ED750JFD77 → JA765EEDA2 → H985KKECB4 → GF950JFB55 → JBAA1IAA92 → IG1KKKKI43 → JHG3KKG432 → IHGCKK7433 → HHEA3GA634 → EEC7KKC867 → ED75KKED77 → FD76KKDD76 → EE85KKEC67 → FE761IED66 → H9885ECCB4 ⮌
114 cycles59 nodes⮎ GC740KJGD85 → KFB94KFB951 → JGA61KIEA42 → JHEA3KGA632 → IGEA3KGA643 → HFCA3KGA854 → HDB71KID974 → JEA63KGEA62 → IGA83KGCA43 → HFC81KIC854 → JEC73KGD862 → IGA74KFDA43 → HEC82KHC864 → IDB63KGE973 → HFA73KGDA54 → HDB82KHC974 → IDA52KHFA73 → IFC82KHC853 → IFC73KGD853 → HFB84KFC954 → GDA72KHDA75 → IC962KHEB83 → IFB62KHE953 → IFC94KFB853 → HEA72KHDA64 → IDB72KHD973 → IFA63KGEA53 → HFB93KGB954 → HDB61KIE974 → JEB73KGD962 → IGA73KGDA43 → HFC92KHB854 → IDC72KHD873 → IFA64KFEA53 → HEA93KGBA64 → HDA50KJFA74 → KFC82KHC851 → JIC73KGD822 → IHF94KFB533 → HFDA5KEA754 → GCA72KHDA85 → IC951KIFB83 → JFD72KHD752 → IHC85KEC833 → HFC63KGE854 → HDB95KEB974 → GC741KIGD85 → JEB94KFB962 → IF951KIFB53 → JFDA5KEA752 → IEA72KHDA63 → IFB72KHD953 → IFC83KGC853 → HFB73KGD954 → HDB83KGC974 → HD952KHFB74 → IDC83KGC873 → HF953KGFB54 → HDBA5KEA974 ⮌
122 cycles21 nodes⮎ D87443GGGDC8 → DCC653GFE888 → DA8543GGFCA8 → DCA53KKGFA88 → HF8731IHDC54 → HEDA63GEA764 → EC885KKECC87 → FD663KKGEE76 → HEA970JDBA64 → JD861KKIEC72 → JIDB60JE9722 → JHG861IEC432 → IGEC83GC8643 → FDC843GGC876 → DC9643GGEB88 → DC8541IGFC88 → HCA543GGFA84 → ECCA3KKGA887 → HD8621IIEC74 → HGD863GEC744 → ECC863GEC887 ⮌
135 cycles8 nodes⮎ HEA852KHFCA64 → IDC961KIEB873 → JFC752KHFD852 → IHCA84KFCA833 → HFD741KIGD754 → JEDB85KEC9762 → IE8752KHFDC63 → IFC974KFDB853 ⮌
145 cycles26 nodes⮎ DA5443KKGGGFA8 → HGCB852HFC9844 → FDCA441IGGA876 → HCC963KKGEB884 → HGB8630JHEC944 → JEDC841IGC8762 → IGC8643GGEC843 → FDCC843GGC8876 → DC96443GGGEB88 → DCC8541IGFC888 → HCA5443GGGFA84 → ECCCA3KKGA8887 → HD86421IIGEC74 → HGDC863GEC8744 → ECC8643GGEC887 → DC87443GGGDC88 → DCC6543GGFE888 → DCA8543GGFCA88 → DCA543KKGGFA88 → HGB8731IHDC944 → HEDC641IGE8764 → HDC8863GECC874 → EC86443GGGEC87 → DCC8743GGDC888 → DC65443GGGFE88 → DCCA853GFCA888 ⮌
152 cycles28 nodes⮎ HEA9751KIFDBA64 → JEC9740KJGDB862 → KHFA752KHFDA531 → JIECA82KHCA8622 → IHGB641KIGE9433 → JFFDCA4KFA87552 → IFAA851KIFCAA53 → JFDA71KKKIDA752 → JIFCB52KHF98522 → IHGCA72KHDA8433 → IFED951KIFB7653 → JFDA973KGDBA752 → IGB8640KJGEC943 → KGECA62KHEA8641 → JIDA861KIECA722 → JHGC751KIFD8432 → JHFDB84KFC97532 → IGDA852KHFCA743 → IFDB851KIFC9753 → JFDA852KHFCA752 → IHCA851KIFCA833 → JFFC741KIGD8552 → JHEBA84KFCA9632 → IGD9630KJHEB743 → KGFDA73KGDA7541 → JHCB862KHEC9832 → IHEB642KHGE9633 → IFEDA84KFCA7653 ⮌
163 cycles26 nodes⮎ DA54443KKGGGGFA8 → HGCCB852HFC98844 → FDCA4441IGGGA876 → HCCC963KKGEB8884 → HGB86430JHGEC944 → JEDCC841IGC88762 → IGC86443GGGEC843 → FDCCC843GGC88876 → DC964443GGGGEB88 → DCCC8541IGFC8888 → HCA54443GGGGFA84 → ECCCCA3KKGA88887 → HD864421IIGGEC74 → HGDCC863GEC88744 → ECC86443GGGEC887 → DCC87443GGGDC888 → DCC65443GGGFE888 → DCCA8543GGFCA888 → DCA5443KKGGGFA88 → HGCB8731IHDC9844 → HEDC6441IGGE8764 → HDCC8863GECC8874 → EC864443GGGGEC87 → DCCC8743GGDC8888 → DC654443GGGGFE88 → DCCCA853GFCA8888 ⮌