Base 26: 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---
23 cycles225×(max) 9 nodes⮎ 0P → O1 → M3 → I7 → AF → 4L → G9 → 6J → CD ⮌
75×3 nodes⮎ 2N → K5 → EB ⮌
25×(fixed) 1 node ⮎ 8H ⮌
31 cycle 3,250×(fixed) (max) 1 node ⮎ CPD ⮌
43 cycles9,658×(max) 6 nodes⮎ 61NK → MDB4 → I1N8 → M9F4 → I5J8 → E9FC ⮌
9,496×(max) 6 nodes⮎ A5JG → E5JC → E1NC → M1N4 → MH74 → I9F8 ⮌
4,571×3 nodes⮎ A1NG → M5J4 → IDB8 ⮌
52 cycles141,780×(max) 4 nodes⮎ H7PH9 → I7PH8 → I9PF8 → H8PG9 ⮌
700×2 nodes⮎ DBPDD → DPPPC ⮌
64 cycles712,337×(max) 9 nodes⮎ E60OJC → OD1NC2 → NL0O43 → OKG852 → MF7HA4 → IA4KF8 → GA4KFA → G64KJA → GD5JCA ⮌
22,188×3 nodes⮎ IG0O98 → OA6IF2 → MC4KD4 ⮌
1,548×(fixed) 1 node ⮎ KE2MB6 ⮌
182×(fixed) 1 node ⮎ DCPPCD ⮌
71 cycle 3,365,830×(max) 4 nodes⮎ JC4PKD7 → LD6PIC5 → KF5PJA6 → KE8PGB6 ⮌
83 cycles10,195,700×(max) 44 nodes⮎ A960OJGG → OD75JIC2 → MEB0OEB4 → OI32MM72 → MKJAE654 → IFD3LCA8 → IA50OKF8 → OFA4KFA2 → MG54KK94 → IGF6IA98 → CA74KIFE → GB51NKEA → MF62MJA4 → KID4KC76 → GEB0OEBA → O632MMJ2 → MKJCC654 → IFCPPCA8 → HF62MJA9 → KD84KHC6 → GE90OGBA → O762MJI2 → MKDAEC54 → IF40OLA8 → OHA4KF82 → MG94KG94 → IG76II98 → CBA6IFEE → C531NMKE → MJF1NA64 → MID4KC74 → IGB0OE98 → OA72MIF2 → MKB4KE54 → IGF2MA98 → KA74KIF6 → GEB4KEBA → G632MMJA → KJD5JC66 → FDD0OCCB → O410OOL2 → ONMG8322 → MLJ7H644 → IHD9FC88 ⮌
3,654,466×5 nodes⮎ JHD0OC87 → OC90OGD2 → OM70OI32 → OMJAE632 → MJD3LC64 ⮌
33,964×2 nodes⮎ KE52MKB6 → KFE2MBA6 ⮌
93 cycles51,977,146×(max) 2 nodes⮎ LG93PLG95 → MGC6PID94 ⮌
473,902×(fixed) 1 node ⮎ LGB4PKE95 ⮌
182×(fixed) 1 node ⮎ DDCPPPCCD ⮌
108 cycles156,972,901×(max) 124 nodes⮎ 64330OMMLK → OJJHDB8662 → MDD91NGCC4 → MI710OOI74 → ONIBAEE722 → MLB42MLE44 → KIHH2M8876 → KEB98GGEB6 → E8732MMIHC → KJB91NGE66 → MED72MICB4 → KIB30OME76 → OJEB2MEB62 → MKD32MMC54 → KJIF0OA766 → OEDB4KECB2 → MG330OMM94 → OJJI6I7662 → MDDCAEDCC4 → I4110OOOL8 → ONNH9F8222 → MLL95JG444 → IHHE6IB888 → CA992MGGFE → K7751NKII6 → MFEBAEEBA4 → I5432MMLK8 → KJHF9FA866 → ED964KJGCC → GD720ONICA → OLB60OJE42 → OMHD2MC832 → MKJ90OG654 → OIFD6ICA72 → MCB50OKED4 → OIF30OMA72 → OMJB4KE632 → MJGD2MC964 → KID70OIC76 → OEBB0OEEB2 → OM332MMM32 → MKJJI66654 → IFDDBDCCA8 → A5210OONKG → ONLF5JA422 → MLHE4KB844 → IHG92MG988 → KA976IIGF6 → ECB74KIEDC → GB320ONMEA → OLJ62MJ642 → MKHDCCC854 → IF90PPOGA8 → PHF80OHA81 → PN994KGG21 → OLG76II942 → MHCB6IED84 → IC930OMGD8 → OJA70OIF62 → OMDB4KEC32 → MJG30OM964 → OJID6IC762 → MDCB0OEDC4 → OI310OOM72 → ONMJAE6322 → MLJD3LC644 → JHHD0OC887 → OC990OGGD2 → OM770OII32 → OMJBAEE632 → MJD42MLC64 → KIHD0OC876 → OEB90OGEB2 → OM732MMI32 → MKJJAE6654 → IFDD3LCCA8 → IA510OOKF8 → ONFA4KFA22 → MLG54KK944 → IHGF6IA988 → CA974KIGFE → GB751NKIEA → MFB62MJEA4 → KID52MKC76 → KFEB0OEBA6 → OE532MMKB2 → MKJF2MA654 → KIFD4KCA76 → GEB50OKEBA → OF632MMJA2 → MKJD4KC654 → IGFD0OCA98 → OA750OKIF2 → OMFB4KEA32 → MJG52MK964 → KIFD6ICA76 → ECB50OKEDC → OF320ONMA2 → OMLJ4K6432 → MJHGCC9864 → ID96PPIGC8 → JH962MJG87 → KDC96IGDC6 → EC710OOIDC → ONB20ONE22 → OMLL2M4432 → MKJHG88654 → IFD97HGCA8 → B9750OKIGF → OFB73LIEA2 → MIB52MKE74 → KIFB2MEA76 → KEB52MKEB6 → KFE32MMBA6 → KJE52MKB66 → KFED2MCBA6 → KE530OMKB6 → OJFE2MBA62 → MKD52MKC54 → KIFF0OAA76 → OEB54KKEB2 → MGF32MMA94 → KJI74KI766 → GEDBAEECBA ⮌
21,064,874×36 nodes⮎ B9510OOKGF → ONF73LIA22 → MLIB4KE744 → IHGB2ME988 → KA972MIGF6 → KEB74KIEB6 → GEB32MMEBA → KJ632MMJ66 → KJEDCCCB66 → ED30PPOMCC → PMCA0OFD31 → PNJ50OK621 → PNLFCCA421 → OLH4PPK842 → NLKD2MC543 → LJHF0OA865 → OGD94KGC92 → MG770OII94 → OIBB6IEE72 → MCB32MMED4 → KJI30OM766 → OJEDAECB62 → MD430OMLC4 → OJIH0O8762 → OMDB8GEC32 → MJ830OMH64 → OJID8GC762 → MDB80OHEC4 → OI930OMG72 → OMJB6IE632 → MJDC2MDC64 → KID10OOC76 → ONEB0OEB22 → OML32MM432 → MKJJG86654 → IFDD7HCCA8 ⮌
2,564,424×10 nodes⮎ JHD10OOC87 → ONC90OGD22 → OML70OI432 → OMJHAE8632 → MJD93LGC64 → JHD70OIC87 → OCB90OGED2 → OM730OMI32 → OMJJAE6632 → MJDD3LCC64 ⮌
2,115,153×6 nodes⮎ EB54PPKKEC → LK97PPHG55 → KKEB0OEB56 → OFE32MMBA2 → MKJ52MK654 → KIFFCCAA76 ⮌
598,005×9 nodes⮎ ECBB0OEEDC → O3320ONMM2 → OMLJI66432 → MJHDBDC864 → ID920ONGC8 → OLA70OIF42 → OMHB4KE832 → MJG92MG964 → KID76IIC76 ⮌
95,775×(fixed) 1 node ⮎ OMJD0OC632 ⮌
95,332×(fixed) 1 node ⮎ KFE52MKBA6 ⮌
72,906×2 nodes⮎ KE552MKKB6 → KFFE2MBAA6 ⮌
114 cycles292,210,468×7 nodes⮎ LGD82PMHC95 → NHD83PLHC83 → MKD94PKGC54 → LIFB3PLEA75 → MGE83PLHB94 → MID84PKHC74 → LIDA4PKFC75 ⮌
280,019,254×5 nodes⮎ LGD93PLGC95 → MGC73PLID94 → MIE93PLGB74 → MIE94PKGB74 → LID94PKGC75 ⮌
15,988,260×(max) 10 nodes⮎ KF963PLJGA6 → MFEA5PJFBA4 → LH953PLKG85 → MGGC7PHD994 → LF873PLIHA5 → MGEA6PIFB94 → LG963PLJG95 → MGFA6PIFA94 → LG964PKJG95 → LGEA6PIFB95 ⮌
12,587,288×5 nodes⮎ LGC61PNJD95 → OIFA3PLFA72 → NLE84PKHB43 → MJHC5PJD864 → LHDB4PKEC85 ⮌
1211 cycles1,372,619,892×(max) 149 nodes⮎ C33320ONMMME → OLJJJ1N66642 → NLHDDCCCC843 → KH910PPOOG86 → POIGB0OE9711 → PNNB72MIE221 → OLLKB2ME5442 → MKHHF2MA8854 → KIF994KGGA76 → GEB774KIIEBA → GBB632MMJEEA → KJD632MMJC66 → KJEDD0OCCB66 → OED310OOMCB2 → ONMJ30OM6322 → OMLJJCC66432 → MJHDCPPCC864 → LJE750OKIB65 → OGFDB2MECA92 → MK7530OMKI54 → OJIFFAEAA762 → MDB553LKKEC4 → JHFF30OMAA87 → OJC954KKGD62 → MGFD70OICA94 → OIB750OKIE72 → OMFBB2MEEA32 → MKJ532MMK654 → KJIFFCCAA766 → EDB54PPKKECC → LK9820ONHG55 → OLGF96IGA942 → MHC774KIID84 → IGBB90OGEE98 → OA7732MMIIF2 → MKJBB4KEE654 → IGFD32MMCA98 → KJA750OKIF66 → OFEDB4KECBA2 → MG5330OMMK94 → OJJIF6IA7662 → MDDCB4KEDCC4 → IG3110OOOM98 → ONNJA6IF6222 → MLLDC4KDC444 → IHHG10OO9888 → ONA996IGGF22 → MLC774KIID44 → IHGBB0OEE988 → OA9732MMIGF2 → MKJB74KIE654 → IGFDB2MECA98 → KA7530OMKIF6 → OJFEB4KEBA62 → MGD532MMKC94 → KJIF70OIA766 → OEDBB4KEECB2 → MG3330OMMM94 → OJJJI6I76662 → MDDDCAEDCCC4 → I41110OOOOL8 → ONNNH9F82222 → MLLL95JG4444 → IHHHE6IB8888 → CA9992MGGGFE → K77751NKIII6 → MFEBBAEEEBA4 → I54332MMMLK8 → KJJHF9FA8666 → EDD964KJGCCC → GD7210OONICA → ONLB60OJE422 → OMLHD2MC8432 → MKJH90OG8654 → OIFD96IGCA72 → MCB750OKIED4 → OIFB30OMEA72 → OMJB52MKE632 → MKJFD2MCA654 → KIFD50OKCA76 → OFEB50OKEBA2 → OMF532MMKA32 → MKJJF4KA6654 → IGFDD4KCCA98 → GA7510OOKIFA → ONFB64KJEA22 → MLGD52MKC944 → KIHF70OIA876 → OEBB94KGEEB2 → MG7332MMMI94 → KJJIB6IE7666 → EDDCB2MEDCCC → K32110OOONM6 → ONNLJDB64222 → MLLHD1NC8444 → MIHH90OG8874 → OIB996IGGE72 → MCB772MIIED4 → KIBB30OMEE76 → OJEB32MMEB62 → MKJD32MMC654 → KJIFD0OCA766 → OEDB50OKECB2 → OMF330OMMA32 → OMJJJ4K66632 → MJGDDCCCC964 → ID710PPOOIC8 → POHG64KJ9811 → ONGD96IGC922 → MLC770OIID44 → OIHBB0OEE872 → OMB932MMGE32 → MKJJ72MI6654 → KIFDDAECCA76 → EB5410OOLKEC → ONHF31NMA822 → NLLJ94KG6443 → KHHGD6IC9886 → EC9970OIGGDC → OB7720ONIIE2 → OMLBB2MEE432 → MKJH32MM8654 → KJIFD8GCA766 → EDB850OKHECC → OF9320ONMGA2 → OMLJ74KI6432 → MJHGDAEC9864 → ID9740OLIGC8 → OHBA70OIFE82 → OMB952MKGE32 → MKJF72MIA654 → KIFDB4KECA76 → GEB530OMKEBA → OJF632MMJA62 → MKJDD4KCC654 → IGFD10OOCA98 → ONA750OKIF22 → OMLFB4KEA432 → MJHG52MK9864 → KIFD96IGCA76 → ECB750OKIEDC → OFB320ONMEA2 → OMLJ52MK6432 → MKJHFCCA8654 → IFD94PPKGCA8 → LHB841NLHE85 → MHG992MGG984 → KI9776IIIG76 → ECBBB6IEEEDC ⮌
216,026,130×48 nodes⮎ A7510PPOOKIG → POJHA1NF8611 → ONMD94KGC322 → MLJG70OI9644 → OIHDB6IEC872 → MCB930OMGED4 → OJI730OMI762 → OMJDBAEEC632 → MJD430OMLC64 → OJIHD0OC8762 → OMDB90OGEC32 → OMJ730OMI632 → OMJJDAEC6632 → MJDD40OLCC64 → OIHD10OOC872 → ONMB90OGE322 → OMLJ72MI6432 → MKJHDAEC8654 → IFD940OLGCA8 → OHA750OKIF82 → OMFB94KGEA32 → MJG752MKI964 → KIFDB6IECA76 → ECB530OMKEDC → OJF320ONMA62 → OMLJD4KC6432 → MJHGD0OC9864 → OID970OIGC72 → OMBB70OIEE32 → OMJB32MME632 → MKJJD2MC6654 → KIFDD0OCCA76 → OEB510OOKEB2 → ONMF32MMA322 → MLKJJ4K66544 → IHGFDCCCA988 → A9750PPOKIGG → PKHB7PPHE851 → OKIC62MJD752 → MKFDB0OECA54 → OIF530OMKA72 → OMJFB4KEA632 → MJGD52MKC964 → KIFD70OICA76 → OEBB50OKEEB2 → OMF332MMMA32 → MKJJJ4K66654 → IGFDDCCCCA98 ⮌
103,570,562×38 nodes⮎ GE5532MMKKBA → KJFF62MJAA66 → KEDD54KKCCB6 → GFE310OOMBAA → ONJ652MKJ622 → MLKFDCCCA544 → IHF50PPOKA88 → PKGC81NHD951 → OMF970OIGA32 → OMJB74KIE632 → MJGDB2MEC964 → KID730OMIC76 → OJEBB0OEEB62 → OMD332MMMC32 → MKJJJ0O66654 → OIFDDCCCCA72 → MB510PPOOKE4 → POKJB5JE6511 → ONFED2MCBA22 → MLK530OMK544 → OJIHFEAA8762 → MDB953LKGEC4 → JHF730OMIA87 → OJCB94KGED62 → MGD730OMIC94 → OJIB70OIE762 → OMDBB2MEEC32 → MKJ330OMM654 → OJJIFCCA7662 → MDDB4PPKECC4 → LLB81PPNHE45 → OLIDA2MFC742 → MKHB50OKE854 → OIFF92MGAA72 → MKB754KKIE54 → IGFFB2MEAA98 → KA7552MKKIF6 → KFFEB4KEBAA6 ⮌
89,685,557×43 nodes⮎ EDC532MMKDCC → KJF210OONA66 → ONLED4KCB422 → MLHG30OM9844 → OJIH96IG8762 → MDCB96IGEDC4 → IC7310OOMID8 → ONJBA0OFE622 → OMLD52MKC432 → MKJHF0OA8654 → OIFD94KGCA72 → MGB750OKIE94 → OIFB72MIEA72 → MKBB52MKEE54 → KIFF32MMAA76 → KJEB54KKEB66 → GFED32MMCBAA → KJ6530OMKJ66 → OJFEDCCCBA62 → MD530PPOMKC4 → PMKHA6IF8531 → OJFC94KGDA62 → MGD750OKIC94 → OIFB70OIEA72 → OMBB52MKEE32 → MKJF32MMA654 → KJIFD4KCA766 → GEDB50OKECBA → OF6330OMMJA2 → OMJJD4KC6632 → MJGDD0OCC964 → OID710OOIC72 → ONMBB0OEE322 → OMLJ32MM6432 → MKJJHCC86654 → IFDD8PPGCCA8 → HH842PPMLH89 → NLED7PPHCB43 → MLGA50OKF944 → OIHF74KIA872 → MGBB94KGEE94 → IG7732MMII98 → KJBBA6IFEE66 ⮌
56,002,324×10 nodes⮎ JHD110OOOC87 → ONNC90OGD222 → OMLL70OI4432 → OMJHHAE88632 → MJD993LGGC64 → JHD770OIIC87 → OCBB90OGEED2 → OM7330OMMI32 → OMJJJAE66632 → MJDDD3LCCC64 ⮌
11,450,580×10 nodes⮎ OMJD10OOC632 → ONMJD0OC6322 → OMLJD0OC6432 → OMJHD0OC8632 → OMJD90OGC632 → OMJD70OIC632 → OMJDB0OEC632 → OMJD30OMC632 → OMJJD0OC6632 → OMJDD0OCC632 ⮌
1,751,737×2 nodes⮎ OMJD50OKC632 → OMJFD0OCA632 ⮌
795,376×5 nodes⮎ JHD710OOIC87 → ONCB90OGED22 → OML730OMI432 → OMJJHAE86632 → MJDD93LGCC64 ⮌
468,984×2 nodes⮎ KFE552MKKBA6 → KFFE52MKBAA6 ⮌
111,646×2 nodes⮎ KE5552MKKKB6 → KFFFE2MBAAA6 ⮌
182×(fixed) 1 node ⮎ DDDCPPPPCCCD ⮌
136 cycles2,193,995,012×15 nodes⮎ MIE952PMKGB74 → NIHD94PKGC873 → MJDA83PLHFC64 → MIFB72PMIEA74 → NIFB83PLHEA73 → MKEA73PLIFB54 → MIGD83PLHC974 → MIEA83PLHFB74 → MIEA73PLIFB74 → MIEB83PLHEB74 → MIEA62PMJFB74 → NIGC83PLHD973 → MKEA83PLHFB54 → MIGC73PLID974 → MIEB93PLGEB74 ⮌
1,241,586,570×(max) 19 nodes⮎ LHFA73PLIFA85 → MGEA74PKIFB94 → LID963PLJGC75 → MGFC93PLGDA94 → MIC762PMJID74 → NIGCB5PJED973 → MIC951PNKGD74 → OJHD93PLGC862 → NLFB83PLHEA43 → MKHD73PLIC854 → MIGDA4PKFC974 → LID962PMJGC75 → NHFC93PLGDA83 → MKD862PMJHC54 → NIHEB4PKEB873 → MJDA62PMJFC64 → NIGD92PMGC973 → NKF973PLIGA53 → MKGD95PJGC954 ⮌
852,690,026×4 nodes⮎ MIFC82PMHDA74 → NIFA72PMIFA73 → NKFB84PKHEA53 → MJFC73PLIDA64 ⮌
822,201,062×13 nodes⮎ LHC973PLIGD85 → MGEA83PLHFB94 → MID863PLJHC74 → MIFCA4PKFDA74 → LID852PMKHC75 → NHGDA4PKFC983 → MJC862PMJHD64 → NIGDB4PKEC973 → MJD951PNKGC64 → OJHEA3PLFB862 → NLFB73PLIEA43 → MKHE83PLHB854 → MIGC95PJGD974 ⮌
191,349,706×5 nodes⮎ LIEB72PMIEB75 → NHEB72PMIEB83 → NKFA62PMJFA53 → NKHE94PKGB853 → MJFC84PKHDA64 ⮌
113,127,894×4 nodes⮎ MIE962PMJGB74 → NIGC94PKGD973 → MJD973PLIGC64 → MIFC93PLGDA74 ⮌
14+---Not showing digit sets 14+ due to verbosity.