Base 23: 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 (fixed) 1 node 7F
31 cycle 2 nodesAMC → BMB
45 cycles11 nodes70LG → L8D2 → J4H4 → FC98 → 72JG → H8D6 → B4HC → D0LA → L2J2 → JG54 → FAB8
51 cycle 4 nodesF6MF8 → G6MF7 → G8MD7 → F7ME8
63 cycles13 nodes720LKG → LI8D42 → JE4H84 → FD5G98 → B73IFC → F80LE8 → L75GF2 → JB7EB4 → F6MMF8 → GDMM87 → FE2J88 → H75GF6 → CA7ECB
71 cycle 8 nodesHB2MJB6 → KD5MG93 → JF6MF74 → ID7ME95 → HB4MHB6 → IB5MGB5 → HD4MH96 → IB7MEB5
83 cycles23 nodesB862JGEC → HA60LGC6 → LBA1KCB2 → KI1MMK43 → LJG1K632 → KIG9C643 → HEA2JC86 → HB61KGB6 → JB9MMCB4 → ID80LE95 → LD63IG92 → JFA3IC74 → GE81KE87 → J965GGD4 → FBA3ICB8 → F71MMKF8 → LFBMMA72 → KFB3IB73 → HF7MME76 → GFA0LC77 → L981KED2 → KI63IG43 → HFE9C876
92 cycles38 nodesHB73MIFB6 → JCA3MICA4 → JF81MKE74 → LGC6MFA62 → KFA4MHC73 → JGA4MHC64 → IFB5MGB75 → HD93MID96 → JC83MIEA4 → JFA3MIC74 → JFB4MHB74 → IFA3MIC75 → JDB4MHB94 → IF81MKE75 → LFB6MFB72 → KF83MIE73 → JHB6MFB54 → IEB3MIB85 → JDA2MJC94 → KFA2MJC73 → KHC4MHA53 → JGC6MFA64 → IDA4MHC95 → ID82MJE95 → KEA4MHC83 → JG93MID64 → JFC6MFA74 → ID84MHE95 → ID94MHD95 → ID83MIE95 → JDA4MHC94 → IF82MJE75 → KEB6MFB83 → JE72MJF84 → KFC6MFA73 → JE84MHE84 → IF95MGD75 → HD95MGD96
104 cycles41 nodes97661KGGFE → JAA84HECC4 → FD621KKG98 → JIA73IFC44 → GEE81KE887 → J9665GGGD4 → FBAA3ICCB8 → F721MMKKF8 → LKDBMMA922 → KKCA1KCA23 → JIH21KK544 → JIFEBA8744 → FE860LGE88 → LA765GGFC2 → JBA81KECB4 → JF61MMKG74 → LIEC0LA842 → LJE61KG832 → KIGA5GC643 → HEBA1KCB86 → JB61MMKGB4 → LIE84HE842 → JED65GG984 → FBA63IGCB8 → FA71MMKFC8 → LFC52JHA72 → JHC81KEA54 → JFC61KGA74 → JFA81KEC74 → JF861KGE74 → JFA85GEC74 → FB861KGEB8 → JA75MMGFC4 → IHC62JGA55 → HDCA1KCA96 → JB421KKIB4 → JIFDMM8744 → IICA1KCA45 → JED21KK984 → JIF63IG744 → GEEA7EC887
115 cycles49 nodesID963MIGD95 → JDC73MIFA94 → JFB62MJGB74 → KFD93MID973 → JHB63MIGB54 → JFDB4MHB974 → IFA61MKGC75 → LFC94MHDA72 → KHA62MJGC53 → KHEB5MGB853 → JFC82MJEA74 → KFC73MIFA73 → JHB84MHEB54 → IFC92MJDA75 → KEB62MJGB83 → KHD82MJE953 → KHE94MHD853 → JGC94MHDA64 → IFB72MJFB75 → KEB83MIEB83 → JHA62MJGC54 → KFEB5MGB873 → JF972MJFD74 → KFC85MGEA73 → JF973MIFD74 → JFB85MGEB74 → IE972MJFD85 → KEB74MHFB83 → JGA72MJFC64 → KFD94MHD973 → JGA63MIGC64 → JFCA5MGCA74 → IE951MKHD85 → LFD94MHD972 → KHA63MIGC53 → JHDB5MGB954 → IEC71MKFA85 → LFB73MIFB72 → KIB83MIEB43 → JHEA2MJC854 → KFE93MID873 → JHB74MHFB54 → IFCA3MICA75 → JDB51MKHB94 → LGE81MKE862 → LJE85MGE832 → KIE85MGE843 → JGD85MGE964 → IEA84MHEC85
123 cycles13 nodesFB8661KGGEB8 → JAA75MMGFCC4 → IHC64MMHGA55 → IHDB73IFB955 → FDC83MMIEA98 → JEA640LIGC84 → LFEA61KGC872 → KIA861KGEC43 → JHEA61KGC854 → JFCA61KGCA74 → JFA821KKEC74 → JIF861KGE744 → JFEA85GEC874
132 cycles83 nodesIEC730MLJFA85 → MIEB73MIFB841 → LJEB72MJFB832 → KJGC72MJFA633 → KHGD94MHD9653 → JGCB73MIFBA64 → JFC950MLHDA74 → MHEA62MJGC851 → LKEB83MIEB822 → KJHA62MJGC533 → KHGEB5MGB8653 → JFCA82MJECA74 → KFC741MKIFA73 → LHGB84MHEB652 → KHCB82MJEBA53 → KHE940MLID853 → MIGD94MHD9641 → LIEB73MIFB842 → KIEB72MJFB843 → KHFB72MJFB753 → KHEA83MIEC853 → JHD963MIGD954 → JFDB73MIFB974 → JFB861MKGEB74 → LGD972MJFD962 → KJD963MIGD933 → JHGC73MIFA654 → JFDB94MHDB974 → IFA641MKIGC75 → LGDC94MHDA962 → KHB742MJIFB53 → KHFDA3MIC9753 → JHDA62MJGC954 → KFEB72MJFB873 → KHC872MJFEA53 → KHEA73MIFC853 → JHDA73MIFC954 → JFDA62MJGC974 → KFD962MJGD973 → KHD963MIGD953 → JHDB73MIFB954 → JFDA61MKGC974 → LGD962MJGD962 → KJDA73MIFC933 → JHGB62MJGB654 → KFEBA4MHCB873 → JGA740MLIFC64 → MHFC94MHDA751 → LICA62MJGCA42 → KJFC61MKGA733 → LHHD94MHD9552 → KHCC83MIEAA53 → JHD941MKID954 → LGFD83MIE9762 → KIC974MHFDA43 → JGEA62MJGC864 → KFDA83MIEC973 → JHB752MJHFB54 → KFECA3MICA873 → JHB741MKIFB54 → LGFDA3MIC9762 → KIC962MJGDA43 → KHFC72MJFA753 → KHEA84MHEC853 → JGC963MIGDA64 → JFCA72MJFCA74 → KFC851MKHEA73 → LHFA73MIFC752 → KIDA84MHEC943 → JGE952MJHD864 → KFEB84MHEB873 → JGA762MJGFC64 → KFDA94MHDC973 → JGA642MJIGC64 → KFFCA5MGCA773 → JF9851MKHED74 → LGEA74MHFC862 → KHB973MIFDB53 → JHDA61MKGC954 → LGEB72MJFB862 → KJD972MJFD933 → KHGC63MIGA653 → JHDBA5MGCB954
145 cycles30 nodesFEB8661KGGEB88 → JAA765MMGGFCC4 → IHD964MMHGD955 → IHDB86MMFEB955 → HHC9631KJGDA56 → JGCBA41KICBA64 → JFEA21MMKKC874 → LKGDB51KHB9622 → KIICA3MMICA443 → JJGE87MMEE8634 → JIDC85MMGEA944 → IIEA740LIFC845 → LEED861KGE9882 → KIA6663IGGGC43 → HFEAAA1KCCC876 → JB86221KKKGEB4 → JIIFA5MMGC7444 → IIFDB62JGB9745 → HEDA83MMIEC986 → JGA9540LIHDC64 → LFECA41KICA872 → KIE8621KKGE843 → JIHEA65GGC8544 → FECBA61KGCBA88 → JA7621MMKKGFC4 → LKGEC62JGA8622 → JIHAA61KGCC544 → JFECA21KKCA874 → JIF8621KKGE744 → JIFEA85GEC8744
155 cycles71 nodesIFCB851MKHEBA75 → LFDA740MLIFC972 → MJHB862MJGEB531 → LKGEB82MJEB8622 → KJID862MJGE9433 → KHGFC84MHEA7653 → JGCB973MIFDBA64 → JFC9630MLJGDA74 → MIFD962MJGD9741 → LKFC963MIGDA722 → KJHC962MJGDA533 → KHGEB72MJFB8653 → KHEB972MJFDB853 → KHEA751MKHFC853 → LHFCA73MIFCA752 → KIDA851MKHEC943 → LHGD952MJHD9652 → KJECB73MIFBA833 → JHGB740MLIFB654 → MHFDB93MIDB9751 → LJDA641MKIGC932 → LJHFC72MJFA7532 → KJGEA84MHEC8633 → JHFB863MIGEB754 → JFDB972MJFDB974 → KFC8641MKIGEA73 → LHGC973MIFDA652 → KIDB962MJGDB943 → KHFC741MKIFA753 → LHGDA84MHEC9652 → KHCB852MJHEBA53 → KHEC940MLIDA853 → MIGD952MJHD9641 → LKFDB73MIFB9722 → KJHB861MKGEB533 → LHHEB82MJEB8552 → KJEC962MJGDA833 → KHGD852MJHE9653 → KHECB84MHEBA853 → JGC9640MLIGDA64 → MHFCA72MJFCA751 → LKEA851MKHEC822 → LJIF963MIGD7432 → KIGEC95MGDA8643 → JGDA852MJHEC964 → KFEB852MJHEB873 → KHEA762MJGFC853 → KHEB973MIFDB853 → JHDA751MKHFC954 → LGECA62MJGCA862 → KJDA841MKIEC933 → LHHFA52MJHC7552 → KJECCA4MHCAA833 → JHF9421MKKID754 → LIGFDA5MGC97642 → KHDA962MJGDC953 → KHEB742MJIFB853 → KHFDA72MJFC9753 → KHEA862MJGEC853 → KHEB863MIGEB853 → JHDB862MJGEB954 → KFEB851MKHEB873 → LHFA762MJGFC752 → KJEB984MHEDB833 → JHF9651MKHGD754 → LGECB95MGDBA862 → KGA8530MLJHEC63 → MIHEB83MIEB8541 → LJED962MJGD9832 → KJGD853MIHE9633 → JHGDB84MHEB9654