Base 23: 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---
21 cycle 176×(fixed) (max) 1 node ⮎ 7F ⮌
31 cycle 2,277×(max) 2 nodes⮎ AMC → BMB ⮌
45 cycles3,087×(max) 11 nodes⮎ 94HE → D4HA → D2JA → H2J6 → HAB6 → B0LC → L0L2 → LI32 → JE74 → F6F8 → 96FE ⮌
3,051×(max) 11 nodes⮎ 52JI → HC96 → B2JC → H0L6 → LAB2 → J0L4 → LE72 → J6F4 → F8D8 → 74HG → D8DA ⮌
3,003×(max) 11 nodes⮎ 30LK → LG52 → JAB4 → F0L8 → L6F2 → J8D4 → F4H8 → D6FA → 92JE → H4H6 → DABA ⮌
2,939×(max) 11 nodes⮎ 50LI → LC92 → J2J4 → HE76 → B6FC → 90LE → L4H2 → JC94 → F2J8 → H6F6 → B8DC ⮌
2,847×(max) 11 nodes⮎ 70LG → L8D2 → J4H4 → FC98 → 72JG → H8D6 → B4HC → D0LA → L2J2 → JG54 → FAB8 ⮌
51 cycle 80,707×(max) 4 nodes⮎ F6MF8 → G6MF7 → G8MD7 → F7ME8 ⮌
63 cycles295,868×(max) 13 nodes⮎ 720LKG → LI8D42 → JE4H84 → FD5G98 → B73IFC → F80LE8 → L75GF2 → JB7EB4 → F6MMF8 → GDMM87 → FE2J88 → H75GF6 → CA7ECB ⮌
41,310×5 nodes⮎ B64HGC → DA0LCA → L31KJ2 → KIF643 → HE8D86 ⮌
39,539×9 nodes⮎ B40LIC → LE0L82 → LJ5G32 → JGAB64 → FA0LC8 → L71KF2 → KI7E43 → HE6F86 → B95GDC ⮌
71 cycle 1,560,757×(max) 8 nodes⮎ HB2MJB6 → KD5MG93 → JF6MF74 → ID7ME95 → HB4MHB6 → IB5MGB5 → HD4MH96 → IB7MEB5 ⮌
83 cycles3,417,438×18 nodes⮎ 861MMKGF → LGC0LA62 → LJA1KC32 → KIG1K643 → JHE9C854 → FC62JGA8 → HA71KFC6 → JB81KEB4 → JF5MMG74 → IHC0LA55 → LDC1KA92 → KI41KI43 → JHED8854 → FC64HGA8 → DA71KFCA → J831KJE4 → JGF5G764 → FBA7ECB8 ⮌
2,397,011×(max) 23 nodes⮎ B862JGEC → HA60LGC6 → LBA1KCB2 → KI1MMK43 → LJG1K632 → KIG9C643 → HEA2JC86 → HB61KGB6 → JB9MMCB4 → ID80LE95 → LD63IG92 → JFA3IC74 → GE81KE87 → J965GGD4 → FBA3ICB8 → F71MMKF8 → LFBMMA72 → KFB3IB73 → HF7MME76 → GFA0LC77 → L981KED2 → KI63IG43 → HFE9C876 ⮌
38,453×5 nodes⮎ B664HGGC → DAA0LCCA → L321KKJ2 → KIIF6443 → HEE8D886 ⮌
92 cycles20,026,034×(max) 38 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 ⮌
134,018×(fixed) 1 node ⮎ JFB3MIB74 ⮌
104 cycles43,763,633×(max) 41 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 ⮌
12,861,309×32 nodes⮎ B8765GGFEC → BA860LGECC → LA620LKGC2 → LJIA1KC432 → KIGE1K8643 → JHEA5GC854 → FCB61KGBA8 → JA71MMKFC4 → LID92JD942 → JHE43II854 → GEEC5GA887 → B9661KGGDC → JAA40LICC4 → LFE21KK872 → KII85GE443 → HEEB5GB886 → CA65MMGGCB → HG64MMHG66 → IGBAMMBB65 → HG84MMHE66 → IGB91KDB65 → JDA3MMIC94 → JIA80LEC44 → LFE61KG872 → KIA85GEC43 → HEB61KGB86 → JBA5MMGCB4 → IH950LHD55 → LDCC3IAA92 → JF421KKI74 → JIFE7E8744 → FE875GFE88 ⮌
7,853,724×20 nodes⮎ B761MMKGFC → LGD52JH962 → JHCA3ICA54 → GEC21KKA87 → JI961KGD44 → JFEA3IC874 → GE861KGE87 → JA965GGDC4 → FBA41KICB8 → JE71MMKF84 → LIDB0LB942 → LJE3MMI832 → KJIB3IB433 → HGFDMM8766 → GGA81KEC67 → JA961KGDC4 → JFA41KIC74 → JFE81KE874 → JF865GGE74 → FBA85GECB8 ⮌
33,551×5 nodes⮎ B6664HGGGC → DAAA0LCCCA → L3221KKKJ2 → KIIIF64443 → HEEE8D8886 ⮌
115 cycles153,755,369×(max) 49 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 ⮌
32,824,404×6 nodes⮎ HD950MLHD96 → MGB83MIEB61 → LJC82MJEA32 → KJGB3MIB633 → JHGC4MHA654 → IFCB5MGBA75 ⮌
4,236,330×5 nodes⮎ IFB61MKGB75 → LFC93MIDA72 → KIB62MJGB43 → KHFC4MHA753 → JGCA4MHCA64 ⮌
1,630,681×5 nodes⮎ IDA51MKHC95 → LFD82MJE972 → KJC74MHFA33 → JHFA4MHC754 → IFCA4MHCA75 ⮌
1,089,913×6 nodes⮎ IEBA3MICB85 → JDA40MLIC94 → MHF92MJD751 → LKEA5MGC822 → KJF83MIE733 → JHGB6MFB654 ⮌
123 cycles530,647,156×(max) 13 nodes⮎ FB8661KGGEB8 → JAA75MMGFCC4 → IHC64MMHGA55 → IHDB73IFB955 → FDC83MMIEA98 → JEA640LIGC84 → LFEA61KGC872 → KIA861KGEC43 → JHEA61KGC854 → JFCA61KGCA74 → JFA821KKEC74 → JIF861KGE744 → JFEA85GEC874 ⮌
17,632,624×(fixed) 1 node ⮎ JFA861KGEC74 ⮌
74,237×5 nodes⮎ B66664HGGGGC → DAAAA0LCCCCA → L32221KKKKJ2 → KIIIIF644443 → HEEEE8D88886 ⮌
132 cycles1,476,237,889×(max) 83 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 ⮌
99,888×2 nodes⮎ IE8543MIIHE85 → JEDD95MGD9984 ⮌
145 cycles2,048,702,804×5 nodes⮎ JFA8621KKGEC74 → JIFA861KGEC744 → JFEA861KGEC874 → JFA8661KGGEC74 → JFAA861KGECC74 ⮌
1,743,052,284×(max) 30 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 ⮌
4,324,118×2 nodes⮎ JFEC63MMIGA874 → JIDB851KHEB944 ⮌
154,868×(fixed) 1 node ⮎ IHD984MMHED955 ⮌
63,103×5 nodes⮎ B666664HGGGGGC → DAAAAA0LCCCCCA → L322221KKKKKJ2 → KIIIIIF6444443 → HEEEEE8D888886 ⮌
155 cycles7,519,813,320×(max) 71 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 ⮌
1,713,457,043×5 nodes⮎ JFC9641MKIGDA74 → LGFC962MJGDA762 → KJDA962MJGDC933 → KHGD742MJIF9653 → KHFDB95MGDB9753 ⮌
94,357,528×(fixed) 1 node ⮎ KHEB862MJGEB853 ⮌
19,282,895×2 nodes⮎ KHEB852MJHEB853 → KHEC962MJGDA853 ⮌
17,288,951×(fixed) 1 node ⮎ KHEC952MJHDA853 ⮌
16+---Not showing digit sets 16+ due to verbosity.