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 nodes⮎ AMC → BMB ⮌
45 cycles11 nodes⮎ 70LG → L8D2 → J4H4 → FC98 → 72JG → H8D6 → B4HC → D0LA → L2J2 → JG54 → FAB8 ⮌
51 cycle 4 nodes⮎ F6MF8 → G6MF7 → G8MD7 → F7ME8 ⮌
63 cycles13 nodes⮎ 720LKG → LI8D42 → JE4H84 → FD5G98 → B73IFC → F80LE8 → L75GF2 → JB7EB4 → F6MMF8 → GDMM87 → FE2J88 → H75GF6 → CA7ECB ⮌
71 cycle 8 nodes⮎ HB2MJB6 → KD5MG93 → JF6MF74 → ID7ME95 → HB4MHB6 → IB5MGB5 → HD4MH96 → IB7MEB5 ⮌
83 cycles23 nodes⮎ B862JGEC → HA60LGC6 → LBA1KCB2 → KI1MMK43 → LJG1K632 → KIG9C643 → HEA2JC86 → HB61KGB6 → JB9MMCB4 → ID80LE95 → LD63IG92 → JFA3IC74 → GE81KE87 → J965GGD4 → FBA3ICB8 → F71MMKF8 → LFBMMA72 → KFB3IB73 → HF7MME76 → GFA0LC77 → L981KED2 → KI63IG43 → HFE9C876 ⮌
92 cycles38 nodes⮎ HB73MIFB6 → 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 nodes⮎ 97661KGGFE → 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 nodes⮎ ID963MIGD95 → 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 nodes⮎ FB8661KGGEB8 → JAA75MMGFCC4 → IHC64MMHGA55 → IHDB73IFB955 → FDC83MMIEA98 → JEA640LIGC84 → LFEA61KGC872 → KIA861KGEC43 → JHEA61KGC854 → JFCA61KGCA74 → JFA821KKEC74 → JIF861KGE744 → JFEA85GEC874 ⮌
132 cycles83 nodes⮎ IEC730MLJFA85 → 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 nodes⮎ FEB8661KGGEB88 → 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 nodes⮎ IFCB851MKHEBA75 → 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 ⮌