Base 24: 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---
22 cycles230×(max) 10 nodes⮎ 0N → M1 → K3 → G7 → 8F → 6H → AD → 2L → I5 → CB ⮌
46×2 nodes⮎ 4J → E9 ⮌
31 cycle 2,576×(fixed) (max) 1 node ⮎ BNC ⮌
41 cycle 17,526×(max) 12 nodes⮎ 7NNG → G6G8 → A7FE → 83JG → G7F8 → 96GF → A5HE → C3JC → FNN8 → F7F9 → 85HG → C7FC ⮌
52 cycles97,658×(fixed) 1 node ⮎ G7NF8 ⮌
598×(max) 2 nodes⮎ CANCC → CNNNB ⮌
65 cycles262,255×4 nodes⮎ A73JGE → G93JE8 → G84IF8 → E86GFA ⮌
94,884×19 nodes⮎ 842KJG → IF7F86 → C86GFC → A6NNGE → HD1LA7 → KA2KD4 → IG2K76 → IC8EB6 → C60MHC → MANNC2 → LD9DA3 → I42KJ6 → IFBB86 → C6NNGC → HB3JC7 → GA0MD8 → M82KF2 → KI6G54 → GD9DA8 ⮌
83,217×(max) 25 nodes⮎ 86NNGG → HENN87 → GF2K88 → I86GF6 → CA6GDC → A2NNKE → LD5HA3 → IC2KB6 → IC0MB6 → MC0MB2 → MK0M32 → MKG632 → KH9D64 → GB3JC8 → G80MF8 → M86GF2 → KA6GD4 → GA2KD8 → I82KF6 → IC6GB6 → CA0MDC → M2NNK2 → LL1L23 → KJH544 → GFBB88 ⮌
34,484×7 nodes⮎ 62NNKI → LH1L63 → KIAC54 → GD1LA8 → K82KF4 → IG6G76 → CA8EDC ⮌
156×(fixed) 1 node ⮎ CBNNBC ⮌
72 cycles1,766,074×(max) 19 nodes⮎ HA4NID7 → JB6NGC5 → ID4NIA6 → JC7NFB5 → IC3NJB6 → KD6NGA4 → JE5NH95 → IE7NF96 → HB5NHC7 → IA5NHD6 → IC6NGB6 → HC4NIB7 → JB5NHC5 → IE5NH96 → IC7NFB6 → HB3NJC7 → KC5NHB4 → JF5NH85 → IE8NE96 ⮌
269,702×(fixed) 1 node ⮎ IC5NHB6 ⮌
83 cycles6,630,118×20 nodes⮎ 6430MKJI → MHFBB862 → KB6NNGC4 → JH93JE65 → GEB4IC98 → E850MIFA → MD73JGA2 → KG92KE74 → IG94IE76 → EC94IEBA → E540MJIA → MFD3JA82 → KG72KG74 → IG98EE76 → C964IHEC → EB4NNICA → JD71LGA5 → KE92KE94 → IG54II76 → EDC8EBAA ⮌
1,254,329×(max) 23 nodes⮎ E742KJGA → IF93JE86 → GC74IGB8 → E980MFEA → M753JIG2 → KGD8EA74 → G962KHE8 → IB84IFC6 → EC70MGBA → M940MJE2 → MKF4I832 → KHE6G964 → GBA4IDC8 → E830MKFA → MH73JG62 → KGB8EC74 → G960MHE8 → MB84IFC2 → KE70MG94 → MG94IE72 → KE94IE94 → GE54II98 → ED84IFAA ⮌
4,254×(fixed) 1 node ⮎ GF7NNF88 ⮌
94 cycles13,619,102×(fixed) 1 node ⮎ JE94NIE95 ⮌
13,067,422×(max) 27 nodes⮎ IC83NJFB6 → KDA3NJDA4 → KG92NKE74 → LGD6NGA73 → KF95NHE84 → JF95NHE85 → IE95NHE96 → IC84NIFB6 → JCA3NJDB5 → KE91NLE94 → MHB4NIC62 → LIC5NHB53 → KGD5NHA74 → JFA5NHD85 → IE94NIE96 → JC94NIEB5 → JE92NKE95 → LFA4NID83 → KHA4NID64 → JGC6NGB75 → ID94NIEA6 → JC93NJEB5 → KEA2NKD94 → LGB3NJC73 → KIC4NIB54 → JGD6NGA75 → ID95NHEA6 ⮌
1,362,096×7 nodes⮎ ID72NKGA6 → LEB5NHC93 → KG82NKF74 → LGD7NFA73 → KE94NIE94 → JG94NIE75 → JEB6NGC95 ⮌
156×(fixed) 1 node ⮎ CCBNNNBBC ⮌
105 cycles49,042,709×(max) 81 nodes⮎ 87430MKJGG → MHF97FE862 → KB874IGFC4 → GE970MGE98 → M9854IIFE2 → KED74IGA94 → GE952KIE98 → ID854IIFA6 → EDC72KGBAA → I9430MKJE6 → MHFC4IB862 → KEB70MGC94 → MG950MIE72 → MKD94IEA32 → KHE52KI964 → IGDB4ICA76 → EC930MKEBA → MH540MJI62 → MKFDACA832 → KH731LKG64 → KHGB8EC764 → GB960MHEC8 → MB850MIFC2 → MKD70MGA32 → MKH92KE632 → KIHB4IC654 → GEDB0MCA98 → M8530MKIF2 → MKHD6GA632 → KHBA2KDC64 → IGB30MKC76 → MHC90MEB62 → MKB50MIC32 → MKHD0MA632 → MKHB2KC632 → KIHB0MC654 → MGDB0MCA72 → MK930MKE32 → MKHH4I6632 → KHEBACC964 → GB520MLIC8 → MJD80MFA42 → MKF72KG832 → KIH96GE654 → GDBA4IDCA8 → E8330MKKFA → MHH73JG662 → KGBB8ECC74 → G9610MMHE8 → MLB84IFC22 → KJE70MG944 → MGF94IE872 → KE974IGE94 → GE954IIE98 → ED854IIFAA → ED742KJGAA → IF942KJE86 → IFC74IGB86 → EC970MGEBA → M9540MJIE2 → MKFD4IA832 → KHE72KG964 → IGB94IEC76 → EC950MIEBA → MD540MJIA2 → MKFD2KA832 → KIH72KG654 → IGDB8ECA76 → C9630MKHEC → MHB4NNIC62 → LJG74IG743 → IFE98EE986 → C7654IIHGC → EDB8NNECAA → FD430MKJA9 → MHF62KH862 → KIBB6GCC54 → GDA10MMDA8 → ML832KKF22 → KJIH6G6544 → GFDB9DCA88 ⮌
38,683,745×40 nodes⮎ CA530MKIDC → MHD2NNKA62 → LLGA3JD723 → JIG92KE755 → IED94IEA96 → EC552KIIBA → IDD40MJAA6 → MFC32KKB82 → KIH70MG654 → MGDB8ECA72 → K9630MKHE4 → MHGB4IC762 → KEB90MEC94 → MG550MII72 → MKDD8EAA32 → KH632KKH64 → IHGBACC766 → CB920MLECC → MJ50NNMI42 → NLIH0M6521 → NLJDACA421 → MJF31LK842 → LJHF6G8643 → IFBA6GDC86 → CA730MKGDC → MH92NNKE62 → LLGB2KC723 → JJH90ME645 → MFEB4IC982 → KE750MIG94 → MGD94IEA72 → KE952KIE94 → IGD54IIA76 → EDC92KEBAA → I5430MKJI6 → MHFDBBA862 → KB72NNKGC4 → LJD93JEA43 → IGF52KI876 → IDC96GEBA6 ⮌
3,996,651×14 nodes⮎ C9764IHGEC → EB94NNIECA → JE831LKF95 → KHE74IG964 → GEB94IEC98 → E8550MIIFA → MDD73JGAA2 → KG932KKE74 → IHG94IE766 → ECB94IECBA → E5410MMJIA → MLFD3JA822 → KJG72KG744 → IGF98EE876 ⮌
835,327×(fixed) 1 node ⮎ MKHB0MC632 ⮌
2,584×(fixed) 1 node ⮎ GG87NNFF78 ⮌
114 cycles175,082,364×(max) 16 nodes⮎ JE961NLHE95 → MGD84NIFA72 → LIB84NIFC53 → KHDA3NJDA64 → KGD72NKGA74 → LGD95NHEA73 → KGA73NJGD74 → KGC95NHEB74 → JFA72NKGD85 → LFC84NIFB83 → KHA73NJGD64 → KGDA5NHDA74 → JFA62NKHD85 → LFD94NIEA83 → KHA63NJHD64 → KGDB6NGCA74 ⮌
108,472,250×11 nodes⮎ JEA63NJHD95 → KED83NJFA94 → KGB63NJHC74 → KGDA4NIDA74 → JGB62NKHC75 → LFDA4NIDA83 → KHA52NKID64 → LGFC6NGB873 → KF983NJFE84 → KGB75NHGC74 → JFA94NIED85 ⮌
2,540,026×(fixed) 1 node ⮎ KGC83NJFB74 ⮌
3,096×(fixed) 1 node ⮎ GFF7NNNF888 ⮌
123 cycles533,144,837×(max) 133 nodes⮎ CB9331LKKECC → KHH50NNMI664 → NJHEBNNB9641 → MJHA62KHD642 → KIFBB2KCC854 → IGD710MMGA76 → MLC992KEEB22 → KJI550MII544 → MGFDDCAAA872 → K97331LKKGE4 → KHHG94IE7664 → GEBB94IECC98 → E85510MMIIFA → MLDD73JGAA22 → KJG932KKE744 → IHGF94IE8766 → ECB974IGECBA → E95410MMJIEA → MLFD53JIA822 → KJGD72KGA744 → IGF992KEE876 → IC9754IIGEB6 → EDC950MIEBAA → MD5430MKJIA2 → MKHFD2KA8632 → KIHB72KGC654 → IGDB90MECA76 → MC9530MKIEB2 → MKHD50MIA632 → MKHDB2KCA632 → KIHB30MKC654 → MHGDB0MCA762 → MKB930MKEC32 → MKHH50MI6632 → MKHDBACCA632 → KHB320MLKC64 → MJHGB0MC7642 → MKFB90MEC832 → MKH750MIG632 → MKHDB8ECA632 → KHB630MKHC64 → MHGBB0MCC762 → MKB910MMEC32 → MLKH50MI6322 → MKJHDACA6432 → KHFB31LKC864 → KHGB70MGC764 → MGB990MEEC72 → MK9550MIIE32 → MKHDD4IAA632 → KHEB32KKC964 → IHGB50MIC766 → MDCB90MECBA2 → MK5310MMKI32 → MLKHHCA66322 → KJHBB1LCC644 → KGFB10MMC874 → MLG970MGE722 → MKJ994IEE432 → KHFE54II9864 → GEDB74IGCA98 → E98530MKIFEA → MHD753JIGA62 → KGDB92KECA74 → IG9530MKIE76 → MHDC94IEBA62 → KEB530MKIC94 → MHGD50MIA762 → MKDB92KECA32 → KIH530MKI654 → MHGDDACAA762 → KB9331LKKEC4 → KHHG50MI7664 → MGDBB8ECCA72 → K96310MMKHE4 → MLHGB4IC7622 → KJEB90MEC944 → MGF550MII872 → MKDD96GEAA32 → KHA532KKID64 → IHGDB2KCA766 → ICB930MKECB6 → MHC510MMIB62 → MLKDB0MCA322 → MKJH30MK6432 → MKHHFAC86632 → KHBB71LGCC64 → KGB910MMEC74 → MLG950MIE722 → MKJD94IEA432 → KHFE52KI9864 → IGDB74IGCA76 → EC9930MKEEBA → MH5540MJII62 → MKFDDACAA832 → KH7331LKKG64 → KHHGB8EC7664 → GBB960MHECC8 → MB8510MMIFC2 → MLKD70MGA322 → MKJH92KE6432 → KIHFB4IC8654 → GEDB70MGCA98 → M98530MKIFE2 → MKHD74IGA632 → KHEB92KEC964 → IGB550MIIC76 → MDDC90MEBAA2 → MK5330MKKI32 → MKHHHCA66632 → KHBBB1LCCC64 → KGB110MMMC74 → MLLG90ME7222 → MKJJ94IE4432 → KHFFE4I98864 → GEB774IGGC98 → E99850MIFEEA → MD7553JIIGA2 → KGDD92KEAA74 → IG9532KKIE76 → IHDC94IEBA66 → ECB530MKICBA → MHD410MMJA62 → MLKFB2KC8322 → KJIH70MG6544 → MGFDB8ECA872 → K97630MKHGE4 → MHGB94IEC762 → KEB950MIEC94 → MGD550MIIA72 → MKDD92KEAA32 → KIH532KKI654 → IHGDDACAA766 ⮌
301,306,783×11 nodes⮎ MKHB10MMC632 → MLKHB0MC6322 → MKJHB0MC6432 → MKHFB0MC8632 → MKHB70MGC632 → MKHB90MEC632 → MKHB50MIC632 → MKHDB0MCA632 → MKHB30MKC632 → MKHHB0MC6632 → MKHBB0MCC632 ⮌
156×(fixed) 1 node ⮎ CCCBNNNNBBBC ⮌
136 cycles951,933,496×4 nodes⮎ KGEB72NKGC974 → LGD972NKGEA73 → LID973NJGEA53 → KIEB73NJGC954 ⮌
942,477,992×(max) 18 nodes⮎ JGDA62NKHDA75 → LFDA62NKHDA83 → LIE952NKIE953 → LIFD94NIEA853 → KHDA63NJHDA64 → KGDB72NKGCA74 → LGD961NLHEA73 → MIFA73NJGD852 → LJEB84NIFC943 → KHFA62NKHD864 → LGEB94NIEC973 → KHB752NKIGC64 → LGFCA4NIDB873 → KHB851NLIFC64 → MHFC93NJEB862 → LJD962NKHEA43 → LIGD83NJFA753 → KIEB84NIFC954 ⮌
242,422,226×2 nodes⮎ KIC862NKHFB54 → LGFC93NJEB873 ⮌
120,106,248×(max) 18 nodes⮎ JEB631NLKHC95 → MIFD82NKFA852 → LKFA74NIGD833 → KIGB84NIFC754 → JGDB83NJFCA75 → KEC851NLIFB94 → MHFA62NKHD862 → LKEB94NIEC933 → KIG952NKIE754 → LGFDB6NGCA873 → KF9851NLIFE84 → MHFA75NHGD862 → LHBA84NIFDC63 → KHC951NLIEB64 → MHFC82NKFB862 → LKE973NJGE933 → KIHC74NIGB654 → JGDCA4NIDBA75 ⮌
53,846,662×2 nodes⮎ KIC852NKIFB54 → LGFDA3NJDA873 ⮌
2,952×(fixed) 1 node ⮎ GGF87NNNFF878 ⮌
1413 cycles1,827,446,544×11 nodes⮎ MKHB310MMKC632 → MLKHHB0MC66322 → MKJHBB0MCC6432 → MKHFB10MMC8632 → MLKHB70MGC6322 → MKJHB90MEC6432 → MKHFB50MIC8632 → MKHDB70MGCA632 → MKHB930MKEC632 → MKHHB50MIC6632 → MKHDBB0MCCA632 ⮌
1,485,425,130×11 nodes⮎ MKHB710MMGC632 → MLKHB90MEC6322 → MKJHB50MIC6432 → MKHFDB0MCA8632 → MKHB730MKGC632 → MKHHB90MEC6632 → MKHBB50MICC632 → MKHDB10MMCA632 → MLKHB30MKC6322 → MKJHHB0MC66432 → MKHFBB0MCC8632 ⮌
1,029,354,319×11 nodes⮎ MKHB510MMIC632 → MLKHDB0MCA6322 → MKJHB30MKC6432 → MKHHFB0MC86632 → MKHBB70MGCC632 → MKHB910MMEC632 → MLKHB50MIC6322 → MKJHDB0MCA6432 → MKHFB30MKC8632 → MKHHB70MGC6632 → MKHBB90MECC632 ⮌
677,808,458×11 nodes⮎ MKHB950MIEC632 → MKHDB50MICA632 → MKHDB30MKCA632 → MKHHB30MKC6632 → MKHHBB0MCC6632 → MKHBB10MMCC632 → MLKHB10MMC6322 → MLKJHB0MC64322 → MKJHFB0MC86432 → MKHFB70MGC8632 → MKHB970MGEC632 ⮌
535,573,489×11 nodes⮎ MKHB530MKIC632 → MKHHDB0MCA6632 → MKHBB30MKCC632 → MKHHB10MMC6632 → MLKHBB0MCC6322 → MKJHB10MMC6432 → MLKHFB0MC86322 → MKJHB70MGC6432 → MKHFB90MEC8632 → MKHB750MIGC632 → MKHDB90MECA632 ⮌
423,969,334×11 nodes⮎ MKHB110MMMC632 → MLLKHB0MC63222 → MKJJHB0MC64432 → MKHFFB0MC88632 → MKHB770MGGC632 → MKHB990MEEC632 → MKHB550MIIC632 → MKHDDB0MCAA632 → MKHB330MKKC632 → MKHHHB0MC66632 → MKHBBB0MCCC632 ⮌
70,980,867×(max) 35 nodes⮎ IGD9510MMIEA76 → MLDC952KIEBA22 → KJID530MKIA544 → MHGFDD2KAA8762 → KIB9732KKGEC54 → IHGD950MIEA766 → MDCB952KIECBA2 → KID5310MMKIA54 → MLHGDD2KAA7622 → KJIB932KKEC544 → IHGFD50MIA8766 → MDCB972KGECBA2 → KI95310MMKIE54 → MLHGDD4IAA7622 → KJEB932KKEC944 → IHGF550MII8766 → MDDCB96GECBAA2 → KA53310MMKKID4 → MLHHGD2KA76622 → KJIBB92KECC544 → IGFD510MMIA876 → MLDC972KGEBA22 → KJI9530MKIE544 → MHGFDD4IAA8762 → KEB9732KKGEC94 → IHG9550MIIE766 → MDDCB94IECBAA2 → KE53310MMKKI94 → MLHHGD4IA76622 → KJEBB92KECC944 → IGF5510MMII876 → MLDDC96GEBAA22 → KJA5330MKKID44 → MHHGFD2KA87662 → KIBB972KGECC54 ⮌
32,949,466×8 nodes⮎ KHEDBB0MCCA964 → MGB5310MMKIC72 → MLKHD90MEA6322 → MKJHB52KIC6432 → KIHFDB0MCA8654 → MGDB730MKGCA72 → MKH9930MKEE632 → MKHHB54IIC6632 ⮌
23,380,257×5 nodes⮎ IG95510MMIIE76 → MLDDC94IEBAA22 → KJE5330MKKI944 → MHHGFD4IA87662 → KEBB972KGECC94 ⮌
108,330×(fixed) 1 node ⮎ JIE994NNIEE955 ⮌
61,554×(fixed) 1 node ⮎ IHCB65NNHHCB66 ⮌
24,780×(fixed) 1 node ⮎ IICC65NNHHBB56 ⮌
4,248×(fixed) 1 node ⮎ GFFF7NNNNF8888 ⮌
15+---Not showing digit sets 15+ due to verbosity.