Base 11: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789A

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 ⮎ 37 ⮌
31 cycle 2 nodes⮎ 4A6 → 5A5 ⮌
42 cycles5 nodes⮎ 3098 → 9452 → 7094 → 9272 → 7454 ⮌
51 cycle 4 nodes⮎ 72A74 → 82A73 → 84A53 → 73A64 ⮌
61 cycle 4 nodes⮎ 531876 → 740964 → 931872 → 863643 ⮌
72 cycles14 nodes⮎ 631A875 → 951A852 → 972A732 → 873A633 → 753A654 → 730A974 → A62A741 → 982A722 → 875A433 → 752A754 → 831A873 → 954A552 → 84AAA53 → 764A544 ⮌
83 cycles7 nodes⮎ 75218854 → 762AA744 → 86309743 → 95418652 → 861AA843 → 97418632 → 86418643 ⮌
92 cycles7 nodes⮎ 871AAA833 → 9770A9332 → A763A6431 → 9741A8632 → 9752A7532 → 8741A8633 → 9552A7552 ⮌
104 cycles11 nodes⮎ 8621AA8843 → 9854186522 → 8661AA8443 → 9743AA6632 → 8762AA7433 → 8753097533 → 9543AA6652 → 8751099533 → 9853AA6522 → 8863097423 → 9654186542 ⮌
113 cycles10 nodes⮎ 85431A87653 → 95530A97552 → A761AAA8431 → 99761A84312 → 98752A75322 → 87641A86433 → 95531A87552 → 9751AAA8532 → 98742A76322 → 87642A76433 ⮌
124 cycles6 nodes⮎ 775310997534 → 98442AA76622 → 88742AA76323 → 885530975523 → 9653AAAA6542 → 87653AA65433 ⮌
132 cycles5 nodes⮎ 984430A976622 → A77531A875331 → 995441A866512 → 987420A986322 → A77652A754331 ⮌
144 cycles17 nodes⮎ 76522218888544 → 766631AA874444 → 974331AA877632 → 98654309765422 → 976421AA886432 → 987542AA765322 → 88753209875323 → 966543AA665442 → 87522109988533 → 986653AA654422 → 88642109986423 → 98665218854422 → 866621AA884443 → 985441AA866522 → 98744109966322 → 98764218864322 → 86664218864443 ⮌
151 cycle 12 nodes⮎ 9844320A9876622 → A776531A8754331 → 9954430A9766512 → A876320A9874321 → A976542A7654311 → 9974320A9876312 → A877542A7653321 → 9864430A9766422 → A775321A8875331 → 9965441A8665412 → 9874220A9886322 → A776652A7544331 ⮌
165 cycles19 nodes⮎ 7665222188885444 → 7666321AA8874444 → 9854331AA8776522 → 9875532098755322 → 976643AAAA664432 → 877652AAAA754333 → 8777422098863333 → 9665444186665442 → 8622221AA8888843 → 9866654186544422 → 8662221AA8888443 → 9866543AA6654422 → 8864221099886423 → 9866652188544422 → 8666221AA8884443 → 9865441AA8665422 → 9874421099866322 → 9876642188644322 → 8666422188864443 ⮌
173 cycles7 nodes⮎ 98644320A98766422 → A7765321A88754331 → 99654430A97665412 → A8763220A98874321 → A9766542A76544311 → 99743220A98876312 → A8776542A76543321 ⮌
186 cycles20 nodes⮎ 76663221AA88874444 → 98654331AA87765422 → 987553310997755322 → 9876443AAAA6664322 → 8877542AAAA7653323 → 887754220988653323 → 96665441AA86654442 → 985422210998886522 → 98766661AA84444322 → 98754321AA88765322 → 987655320987554322 → 9766441AAAA8664432 → 9876542AAAA7654322 → 88875421AA88653223 → 986655420986554422 → 9766221AAAA8884432 → 988864420986642222 → 976666221888444432 → 866642221888864443 → 766652221888854444 ⮌
193 cycles5 nodes⮎ 998654320A987654212 → A87765320A987543321 → A97654430A976654311 → A98643220A988764211 → A98766531A875443211 ⮌
206 cycles8 nodes⮎ 88775431AAAA87653323 → 98775542209886553322 → 97666441AAAA86644432 → 98765431AAAA87654322 → 988764421AA886643222 → 987665431AA876544322 → 98755332109987755322 → 98766443AAAA66644322 ⮌
214 cycles2 nodes⮎ AA98754320A9876532101 → AA98765430A9765432101 ⮌
227 cycles24 nodes⮎ 7665222222188888885444 → 7666666321AA8874444444 → 9854332221AA8888776522 → 9876665532098755444322 → 976644221AAAA888664432 → 988864442AAAA766642222 → 888874442AAAA766632223 → 8888554430AA9766552223 → A876554310AA9976554321 → A997653310AA9977543111 → A998866432098764422111 → A888666422188864442221 → 9766666222188884444432 → 8666642222188888644443 → 7666652222188888544444 → 7666632221AA8888744444 → 9866543321AA8877654422 → 9876553321099877554322 → 987664441AAAA866644322 → 988754431AAAA876653222 → 9888654421AA8866542222 → 9876664421099866444322 → 9876642222188888644322 → 8666666422188864444443 ⮌
236 cycles2 nodes⮎ AAA98754320A98765321001 → AAA98765430A97654321001 ⮌
247 cycles12 nodes⮎ 88887544320AA98766532223 → A87665553310997755544321 → A88644421AAAAAA886664221 → 99888664421AA88664422212 → 99776664421AA88664443312 → 99775533221AA88877553312 → 99776554421AA88665543312 → 99775533210AA99877553312 → A9877654421AA88665433211 → 999765533210998775543112 → 9888764441AAAA8666432222 → 9888754442AAAA7666532222 ⮌
259 cycles2 nodes⮎ AAAA98754320A987653210001 → AAAA98765430A976543210001 ⮌
2610 cycles22 nodes⮎ 888875443310AA997766532223 → A9776555433109977655543311 → A888444421AAAAAA8866662221 → 998888644421AA886664222212 → 997766664421AA886644443312 → 997755332221AA888877553312 → 997766554421AA886655443312 → 997755332210AA998877553312 → A98777554421AA886655333211 → 999765543310AA997765543112 → A98876643310AA997764432211 → A99877554331AA877655332111 → 999875544320AA987665532112 → A98777553310AA997755333211 → A99876544421AA886665432111 → 99987654322109988765432112 → 988876664421AA886644432222 → 987666543221AA888765444322 → 98766553322109988775544322 → 98766644421AAAA88666444322 → 98886444321AAAA88766642222 → 98887654442AAAA76665432222 ⮌
2714 cycles2 nodes⮎ AAAAA98754320A9876532100001 → AAAAA98765430A9765432100001 ⮌
2810 cycles45 nodes⮎ 8888754433210AA9987766532223 → A977665554331099776555443311 → A8884444221AAAAAA88866662221 → 9988888444421AA8866662222212 → 9977666664421AA8866444443312 → 9977553322221AA8888877553312 → 9977666554421AA8866554443312 → 9977553322210AA9988877553312 → A987776554421AA8866554333211 → 9997655433210AA9987765543112 → A988776543310AA9977654332211 → A998775544331099776655332111 → A88886444421AAAA886666422221 → 998886644441AAAA866664422212 → 998877444421AAAA886666332212 → 998877554432AAAA776655332212 → 9888765533221099887755432222 → 987666664441AAAA866644444322 → 988754432221AAAA888876653222 → 9888766554421AA8866554432222 → 9876665432210AA9988765444322 → A977765533221099887755433311 → A88866444441AAAA866666442221 → 998884444221AAAA888666622212 → 998877664443AAAA666644332212 → 988866543321AAAA887765442222 → 9888765544320AA9876655432222 → A877665533210AA9987755443321 → A997755443310AA9977665533111 → A998866443310AA9977664422111 → A998877553321AA8877553322111 → 9998766554421AA8866554432112 → 9987765432210AA9988765433212 → A987776554331099776554333211 → A88864444421AAAA886666642221 → 998886444421AAAA886666422212 → 998877644441AAAA866664332212 → 998876544331AAAA877665432212 → 9988765543320AA9877655432212 → A977765543310AA9977655433311 → A998664443310AA9977666442111 → A998876533221AA8887754322111 → 9998766655432098765544432112 → 988766442221AAAA888866443222 → 988876654442AAAA766654432222 ⮌
2920 cycles16 nodes⮎ 9888877444420AAA9866663322222 → A887766554331AAA8776554433221 → 99885554333110A99977765552212 → A88877654430AAAAA976654332221 → A988876544321AAA8876654322211 → 99987665543310A99776554432112 → A888775443220AAA9887665332221 → A9887665553320A98775554432211 → A98766544320AAAAA987665443211 → A998876544320AAA9876654322111 → A9997775543310A99776553331111 → A988886444430AAA9766664222211 → A998776544321AAA8876654332111 → 99997755533310A99777555331112 → A88887644441AAAAA866664322221 → 998888544442AAAAA766665222212 ⮌
3011 cycles17 nodes⮎ 88887544332210AA99887766532223 → A97766655543310997765554443311 → A88844442221AAAAAA888866662221 → 99888886444421AA88666642222212 → 99776666644221AA88866444443312 → 99776553322221AA88888775543312 → 99776665544320AA98766554443312 → A9776543322210AA99888776543311 → A99877655443310997766554332111 → A888864444221AAAA8886666422221 → 9988866644441AAAA8666644422212 → 9988774444221AAAA8886666332212 → 9988776554432AAAA7766554332212 → 988876553332110999877755432222 → 9887666644441AAAA8666644443222 → 9888644432221AAAA8888766642222 → 9888766654442AAAA7666544432222 ⮌
3127 cycles6 nodes⮎ 999987655433310A997776554321112 → A8888775444320AAA98766653322221 → A98876655533310A997775554432211 → A988765444320AAAAA9876665432211 → A9988866444320AAA98766644222111 → A9997776544321AAA88766543331111 ⮌
3212 cycles15 nodes⮎ 98887544432221AAAA88887666532222 → 988876665544320AA987665544432222 → A87766553322210AA998887755443321 → A99776655443310AA997766554433111 → A99886644332210AA998877664422111 → A99887766553321AA887755443322111 → 999876655443310AA997766554432112 → A98877654332210AA998877654332211 → A9987766554433109977665544332111 → A8888644442221AAAA88886666422221 → 99888666644441AAAA86666444422212 → 99887744442221AAAA88886666332212 → 99887766554432AAAA77665544332212 → 98887655333311109999777755432222 → 98887666444441AAAA86666644432222 ⮌
3335 cycles2 nodes⮎ AAAAAAAA98754320A9876532100000001 → AAAAAAAA98765430A9765432100000001 ⮌
3412 cycles12 nodes⮎ 888888754444320AAAA987666653222223 → A888766555443310AA9977665554432221 → A99776554332210AAAA998877655433111 → A999977665533221099887755443311111 → A88888866444421AAAA886666442222221 → 998886666444421AAAA886666444422212 → 998877644442221AAAA888866664332212 → 998877665544331AAAA877665544332212 → 9988765553333111099997777555432212 → 98888766444441AAAAAA86666644322222 → 98888864444431AAAAAA87666664222222 → 98888875444442AAAAAA76666653222222 ⮌
3546 cycles2 nodes⮎ AAAAAAAAA98754320A98765321000000001 → AAAAAAAAA98765430A97654321000000001 ⮌
3615 cycles4 nodes⮎ 532222222222222221888888888888888876 → 766666666666666640964444444444444444 → 932222222222222221888888888888888872 → 866666666666666663644444444444444443 ⮌
3760 cycles3 nodes⮎ A988887654444430AAAAA9766666543222211 → A9988876544433210AAA99877666543222111 → A99987776555333210A998777555433321111 ⮌
3818 cycles6 nodes⮎ 99998887644444310AAAA99766666432221112 → A9998777765443321AAAA88776654333321111 → 999997765554433320AA987776655543311112 → A9888776544433210AAAA99877666543322211 → A99987775555333310AA997777555533321111 → A998887654444421AAAAAA8866666543222111 ⮌
3974 cycles6 nodes⮎ A9888887544444320AAAAA98766666532222211 → A99888776554443310AAA997766655433222111 → A999877755543332110A9998777655533321111 → A9888887654444430AAAAA97666665432222211 → A99888775544433210AAA998776665533222111 → A999877765554333110A9997776555433321111 ⮌