Base 22: 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 231×(max) 11 nodes⮎ 0L → K1 → I3 → E7 → 6F → 8D → 4H → C9 → 2J → G5 → AB ⮌
31 cycle 2,002×(fixed) (max) 1 node ⮎ ALB ⮌
42 cycles6,545×(max) 5 nodes⮎ A1JC → I1J4 → ID74 → E5F8 → A5FC ⮌
6,083×(max) 5 nodes⮎ 61JG → I9B4 → E1J8 → I5F4 → E9B8 ⮌
53 cycles41,826×3 nodes⮎ E5LF8 → G6LE6 → F9LB7 ⮌
23,428×(max) 4 nodes⮎ E6LE8 → F5LF7 → G7LD6 → F8LC7 ⮌
504×2 nodes⮎ B9LBB → BLLLA ⮌
63 cycles279,381×(max) 21 nodes⮎ 420KJI → KHD742 → ID5F84 → EA4GB8 → C60KFA → K91JC2 → JH2I43 → HFC865 → C93HCA → E31JI8 → IF5F64 → EA8CB8 → 640KHG → KD9B82 → I51JG4 → IEAA74 → E6LLE8 → FCLL87 → ED2I88 → G64GF6 → CA8CBA ⮌
16,475×12 nodes⮎ 864GFE → C95FCA → A31JIC → IF1J64 → IE8C74 → E73HE8 → E75FE8 → A75FEC → A71JEC → I71JE4 → IE6E74 → E86ED8 ⮌
132×(fixed) 1 node ⮎ BALLAB ⮌
71 cycle 1,184,018×(max) 4 nodes⮎ GA3LHB6 → IB5LFA4 → HD4LG85 → HC7LD95 ⮌
82 cycles4,269,125×(max) 75 nodes⮎ 6432IIHG → GFD9B866 → A951JGCC → IB31JIA4 → IFE0K764 → KE96EC72 → I872IED4 → GE74GE76 → CA76EEBA → 8720KJEE → KH75FE42 → IDA6EB84 → E850KGD8 → KB64GFA2 → IC90KC94 → KE32II72 → IGF6E654 → EB97DCA8 → 7530KIGF → KFB7DA62 → I960KFC4 → KE92IC72 → IG72IE54 → GEB6EA76 → A870KEDC → K751JGE2 → JHB6EA43 → GD80KD86 → KA54GGB2 → ICB0KA94 → KE30KI72 → KIF6E632 → IF97DC64 → E962IFC8 → G962IFC6 → GA92ICB6 → GA30KIB6 → KFA0KB62 → KI90KC32 → KIF2I632 → IGF8C654 → EB93HCA8 → E630KIF8 → KF95FC62 → IA92ICB4 → GE30KI76 → KFA6EB62 → I980KDC4 → KE52IG72 → IGB6EA54 → EB80KDA8 → K650KGF2 → KIB8CA32 → IF40KH64 → KED8C872 → I753HGE4 → FDB6EA87 → 9750KGED → KB73HEA2 → IE70KE74 → KE76EE72 → I876EED4 → E874GED8 → C764GFEA → C971JECA → I731JIE4 → IFE6E764 → E986EDC8 → 8652IGFE → GB95FCA6 → B930KICB → KF2LLI62 → JJE2I723 → HHF6E645 → DC97DC99 ⮌
22,998×7 nodes⮎ C540KHGA → KDB1JA82 → JH50KG43 → KGDAA852 → IB4LLGA4 → HH84GD45 → DDB4GA89 ⮌
93 cycles13,983,072×(max) 21 nodes⮎ GC84LGD96 → HA83LHDB5 → IC92LIC94 → JE92LIC73 → JGB4LGA53 → IFB5LFA64 → HD94LGC85 → HC83LHD95 → IC93LHC94 → IE82LID74 → JEB5LFA73 → IE83LHD74 → IEA5LFB74 → HD83LHD85 → IC94LGC94 → HE72LIE75 → JDA6LEB83 → ID62LIF84 → JEC6LE973 → ID74LGE84 → HE95LFC75 ⮌
323,924×(fixed) 1 node ⮎ IEA3LHB74 ⮌
132×(fixed) 1 node ⮎ BBALLLAAB ⮌
102 cycles25,175,365×(max) 39 nodes⮎ 86330KIIFE → KFF95FC662 → IA992ICCB4 → GE330KII76 → KFFA6EB662 → I9980KDCC4 → KE532IIG72 → IGFB6EA654 → EB980KDCA8 → K6530KIGF2 → KIFB8CA632 → IF940KHC64 → KED92IC872 → IG752IGE54 → GEBB6EAA76 → A8710KKEDC → KJ751JGE22 → JHHB6EA443 → GDD80KD886 → KA554GGGB2 → ICBB0KAA94 → KE310KKI72 → KJIF6E6322 → IHF97DC644 → ED962IFC88 → G9652IGFC6 → GBA92ICBA6 → GA310KKIB6 → KJFA0KB622 → KIH90KC432 → KIFD2I8632 → IGF94GC654 → ECB92ICA98 → G6330KIIF6 → KFFA8CB662 → I9940KHCC4 → KED32II872 → IGF74GE654 → ECB96ECA98 ⮌
19,176,778×14 nodes⮎ CA310KKIBA → KJF20KJ622 → KIHH8C4432 → IFDD3H8864 → FD954GGC87 → CB852IGDAA → GB520KJGA6 → KHBA0KBA42 → KID10KK832 → KJIF4G6322 → IHFC8C9644 → ED942IHC88 → GD652IGF86 → GBA94GCBA6 ⮌
114 cycles56,876,688×(max) 8 nodes⮎ HE951LJGC75 → KEC94LGC972 → JG952LIGC53 → JGDB6LEA853 → IEA62LIFB74 → JEC83LHD973 → IGA63LHFB54 → IECA4LGB974 ⮌
42,061,846×3 nodes⮎ IEC82LID974 → JEB63LHFA73 → IGB83LHDA54 ⮌
23,520,388×(max) 8 nodes⮎ HD862LIFD85 → JDB74LGEA83 → IF962LIFC64 → JEC95LFC973 → IE852LIGD74 → JED95LFC873 → IE863LHFD74 → IEB85LFDA74 ⮌
6,565,536×(fixed) 1 node ⮎ IEA73LHEB74 ⮌
123 cycles317,955,722×(max) 70 nodes⮎ 865330KIIGFE → KFFB95FCA662 → IA9930KICCB4 → KFE330KII762 → KIFF96EC6632 → IF9982IDCC64 → GE9532IIGC76 → GFBA72IEBA66 → GA9710KKECB6 → KJA730KIEB22 → KIHF70KE6432 → KIFD96EC8632 → IF9852IGDC64 → GEB952IGCA76 → GBA730KIEBA6 → KFA710KKEB62 → KJI970KEC322 → KIHF72IE6432 → IGFD96EC8654 → EB9852IGDCA8 → GB6530KIGFA6 → KFBA90KCBA62 → KI9310KKIC32 → KJIFF2I66322 → IHGF98CC6544 → EDB942IHCA88 → GD6530KIGF86 → KFBA94GCBA62 → IC9310KKIC94 → KJFE32II7622 → IHGF96EC6544 → EDB982IDCA88 → G65530KIGGF6 → KFBBA8CBAA62 → I94110KKKHC4 → KJJED2I87222 → IHHG74GE5444 → EDDCB6EA9888 → 865530KIGGFE → KFBB95FCAA62 → IA9310KKICB4 → KJFE30KI7622 → KIHF96EC6432 → IFD982IDC864 → GE9552IGGC76 → GBBA72IEBAA6 → GA7110KKKEB6 → KJJA70KEB222 → KIHH70KE4432 → KIFDD6E88632 → IF9854GGDC64 → ECB952IGCA98 → GB6330KIIFA6 → KFFA90KCB662 → KI9930KICC32 → KIFF32II6632 → IGFF98CC6654 → EB9942IHCCA8 → GD6330KIIF86 → KFFA94GCB662 → IC9930KICC94 → KFE332III762 → IGFF96EC6654 → EB9982IDCCA8 → G65330KIIGF6 → KFFBA8CBA662 → I99410KKHCC4 → KJED32II8722 → IHGF74GE6544 → EDCB96ECA988 ⮌
36,861,444×39 nodes⮎ 863330KIIIFE → KFFF95FC6662 → IA9992ICCCB4 → GE3330KIII76 → KFFFA6EB6662 → I99980KDCCC4 → KE5332IIIG72 → IGFFB6EA6654 → EB9980KDCCA8 → K65330KIIGF2 → KIFFB8CA6632 → IF9940KHCC64 → KED932IIC872 → IGF752IGE654 → GEBB96ECAA76 → A87310KKIEDC → KJF751JGE622 → JHHB96ECA443 → GDD830KID886 → KFA554GGGB62 → ICBB90KCAA94 → KE3310KKII72 → KJIFF6E66322 → IHF997DCC644 → ED9632IIFC88 → GF9652IGFC66 → GBA992ICCBA6 → GA3310KKIIB6 → KJFFA0KB6622 → KIH990KCC432 → KIFD32II8632 → IGFF94GC6654 → ECB992ICCA98 → G63330KIIIF6 → KFFFA8CB6662 → I99940KHCCC4 → KED332III872 → IGFF74GE6654 → ECB996ECCA98 ⮌
132×(fixed) 1 node ⮎ BBBALLLLAAAB ⮌
135 cycles706,020,614×(max) 43 nodes⮎ HEBA61LJFBA75 → KEB840LKHDA72 → LIGA62LIFB531 → KJFDA4LGB8622 → JIFA72LIEB633 → JGFC83LHD9653 → IGCA73LHEB954 → IEC951LJGC974 → KFD952LIGC862 → JIDA73LHEB833 → IGFA62LIFB654 → JEDA94LGCB873 → IF9641LJHFC64 → KFEB95LFCA762 → JF9851LJGDC63 → KGEA73LHEB752 → JHC973LHEC943 → IGDA52LIGB854 → JEDB82LIDA873 → JGB652LIGFA53 → JGDBA4LGBA853 → IFB830LKIDA64 → LHEC72LIE9741 → KJEA74LGEB722 → JIF973LHEC633 → IGFB84LGDA654 → HEBA72LIEBA75 → JDA740LKHEB83 → LHFA62LIFB641 → KJEB94LGCA722 → JIF951LJGC633 → KGGDA5LFB8552 → JFBB72LIEAA63 → JGC840LKHD953 → LHFC83LHD9641 → KIDB73LHEA832 → JHFA62LIFB643 → JGEB94LGCA753 → IFB951LJGCA64 → KFDA61LJFB862 → KID972LIEC832 → JIFB63LHFA633 → IGFB94LGCA654 ⮌
219,479,540×4 nodes⮎ IGC962LIFC954 → JEDA62LIFB873 → JGC862LIFD953 → JGDA73LHEB853 ⮌
1,293,350×6 nodes⮎ HEB940LKHCA75 → LGCA51LJGB951 → KKEB71LJEA712 → KJIC73LHE9322 → JIGFA4LGB6533 → IGEBA4LGBA754 ⮌
970,794×2 nodes⮎ IE8652LIGFD74 → JEDA85LFDB873 ⮌
219,440×(fixed) 1 node ⮎ IEA773LHEEB74 ⮌
148 cycles2,028,789,468×(max) 50 nodes⮎ EB99832IIDCCA8 → GF65330KIIGF66 → KFFBA98CCBA662 → I994310KKIHCC4 → KJFED32II87622 → IHGF974GEC6544 → EDCB972IECA988 → G765330KIIGFE6 → KFFBA96ECBA662 → I998310KKIDCC4 → KJFE532IIG7622 → IHGFB96ECA6544 → EDB9830KIDCA88 → KF65530KIGGF62 → KIFBB98CCAA632 → IF94310KKIHC64 → KJFED92IC87622 → IHG9752IGEC544 → GEDBB72IEAA876 → GA77510KKGEEB6 → KJBA770KEEBA22 → KIH7710KKEE432 → KJIFD76EE86322 → IHF9874GEDC644 → EDC9752IGEC988 → GB76532IIGFEA6 → GFBA970KECBA66 → KA97310KKIECB2 → KJIF730KIE6322 → KIHFF96EC66432 → IFD9982IDCC864 → GE95532IIGGC76 → GFBBA72IEBAA66 → GA97110KKKECB6 → KJJA730KIEB222 → KIHHF70KE64432 → KIFDD96EC88632 → IF98552IGGDC64 → GEBB952IGCAA76 → GBA7310KKIEBA6 → KJFA710KKEB622 → KJIH970KEC4322 → KIHFD72IE86432 → IGFD974GEC8654 → ECB9752IGECA98 → GB76330KIIFEA6 → KFFA970KECB662 → KI99730KIECC32 → KIFF732IIE6632 → IGFF996ECC6654 ⮌
174,514,543×26 nodes⮎ EB98552IGGDCA8 → GBB6530KIGFAA6 → KFBA910KKCBA62 → KJI9310KKIC322 → KJIHFF2I664322 → IHGFD98CC86544 → EDB9542IHGCA88 → GDB6530KIGFA86 → KFBA950KGCBA62 → KIB9310KKICA32 → KJIFF30KI66322 → KIHFF98CC66432 → IFD9942IHCC864 → GED9532IIGC876 → GFBA752IGEBA66 → GBA9710KKECBA6 → KJA7310KKIEB22 → KJIHF70KE64322 → KIHFD96EC86432 → IFD9852IGDC864 → GEB9552IGGCA76 → GBBA730KIEBAA6 → KFA7110KKKEB62 → KJJI970KEC3222 → KIHHF72IE64432 → IGFDD96EC88654 ⮌
89,620,701×39 nodes⮎ 8633330KIIIIFE → KFFFF95FC66662 → IA99992ICCCCB4 → GE33330KIIII76 → KFFFFA6EB66662 → I999980KDCCCC4 → KE53332IIIIG72 → IGFFFB6EA66654 → EB99980KDCCCA8 → K653330KIIIGF2 → KIFFFB8CA66632 → IF99940KHCCC64 → KED9332IIIC872 → IGFF752IGE6654 → GEBB996ECCAA76 → A873310KKIIEDC → KJFF751JGE6622 → JHHB996ECCA443 → GDD8330KIID886 → KFFA554GGGB662 → ICBB990KCCAA94 → KE33310KKIII72 → KJIFFF6E666322 → IHF9997DCCC644 → ED96332IIIFC88 → GFF9652IGFC666 → GBA9992ICCCBA6 → GA33310KKIIIB6 → KJFFFA0KB66622 → KIH9990KCCC432 → KIFD332III8632 → IGFFF94GC66654 → ECB9992ICCCA98 → G633330KIIIIF6 → KFFFFA8CB66662 → I999940KHCCCC4 → KED3332IIII872 → IGFFF74GE66654 → ECB9996ECCCA98 ⮌
20,611,319×14 nodes⮎ FD95532IIGGC87 → GFBB852IGDAA66 → GBA9510KKGCBA6 → KJBA310KKIBA22 → KJIHF10KK64322 → KJIHFD8C864322 → IHFD953HGC8644 → FDDB952IGCA887 → GB85530KIGGDA6 → KFBBA50KGBAA62 → KIB9110KKKCA32 → KJJIF30KI63222 → KIHHFF8C664432 → IFDD993HCC8864 ⮌
5,195,456×7 nodes⮎ FDD9552IGGC887 → GBB8552IGGDAA6 → GBBA510KKGBAA6 → KJBA110KKKBA22 → KJJIH10KK43222 → KJIHHFC8644322 → IHFDD93HC88644 ⮌
696,109×(fixed) 1 node ⮎ LJHDB50KGA8421 ⮌
415,728×2 nodes⮎ HHC953LLHGC945 → IHCC86LLED9944 ⮌
116,054×(fixed) 1 node ⮎ HGC974LLGEC955 ⮌
159 cycles3,518,952,376×16 nodes⮎ IGE8530LKIGD754 → LHEDB95LFCA8741 → KHC8641LJHFD942 → KIFDB73LHEA8632 → JHFB862LIFDA643 → JGEB972LIECA753 → JGD9751LJGEC853 → KGEB963LHFCA752 → JHCA851LJGDB943 → KGFC841LJHD9652 → KIFCA73LHEB9632 → JHFB851LJGDA643 → KGFCA72LIEB9652 → JIDA851LJGDB833 → KGGD852LIGD8552 → JIDBB84LGDAA833 ⮌
968,301,958×(max) 24 nodes⮎ IEC9531LJIGC974 → KGED952LIGC8752 → JIDB963LHFCA833 → IGFB741LJHEA654 → KFECA83LHDB9762 → JHB8641LJHFDA43 → KGFDB72LIEA8652 → JIDA862LIFDB833 → JGFC752LIGE9653 → JGDBA84LGDBA853 → IFB8530LKIGDA64 → LHEDA72LIEB8741 → KJEA762LIFEB722 → JIHC873LHED9433 → IGFDA63LHFB8654 → IECA972LIECB974 → JEB7531LJIGEA73 → KGGD973LHEC8552 → JHCB963LHFCA943 → IGDB631LJIFA854 → KGEDA72LIEB8752 → JID9762LIFEC833 → JGFC863LHFD9653 → IGCA973LHECB954 ⮌
561,140,574×6 nodes⮎ JGEB631LJIFA753 → KGGDA83LHDB8552 → JHCB852LIGDA943 → JGEC841LJHD9753 → KGFC963LHFC9652 → JHCA962LIFCB943 ⮌
236,084,460×11 nodes⮎ IFA8641LJHFDB64 → KFEB972LIECA762 → JIC8751LJGED933 → KGGD963LHFC8552 → JHCBA73LHEBA943 → IGDA520LKJGB854 → LIFDB82LIDA8631 → KJFC752LIGE9622 → JIHDA84LGDB8433 → IGED852LIGD8754 → JEDB964LGFCA873 ⮌
189,834,966×10 nodes⮎ IFB9641LJHFCA64 → KFEB961LJFCA762 → KID9851LJGDC832 → KIGD853LHGD8532 → JHFCB84LGDA9643 → IFDA741LJHEB864 → KFEB862LIFDA762 → JIC9862LIFDC933 → JGFC742LIHE9653 → JGECA84LGDB9753 ⮌
91,460,878×(fixed) 1 node ⮎ JGDB852LIGDA853 ⮌
1,906,538×2 nodes⮎ IE87652LIGFED74 → JEDA875LFEDB873 ⮌
220,656×(fixed) 1 node ⮎ IEA7773LHEEEB74 ⮌
132×(fixed) 1 node ⮎ BBBBALLLLLAAAAB ⮌
16+---Not showing digit sets 16+ due to verbosity.