Base 17: 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 cycles96×(max) 3 nodes⮎ 1F → D3 → 97 ⮌
32×(fixed) 1 node ⮎ 5B ⮌
31 cycle 952×(max) 2 nodes⮎ 7G9 → 8G8 ⮌
48 cycles812×(max) 4 nodes⮎ 30FE → FA52 → D4B4 → 9698 ⮌
744×(max) 4 nodes⮎ 90F8 → F0F2 → FC32 → D874 ⮌
703×(max) 4 nodes⮎ 72DA → B2D6 → B4B6 → 74BA ⮌
667×(max) 4 nodes⮎ 50FC → F692 → D2D4 → B876 ⮌
641×(max) 4 nodes⮎ 70FA → F2D2 → DA54 → 94B8 ⮌
564×(max) 4 nodes⮎ 92D8 → B0F6 → F4B2 → D694 ⮌
419×2 nodes⮎ 52DC → B696 ⮌
278×2 nodes⮎ D0F4 → F872 ⮌
51 cycle 20,332×(max) 4 nodes⮎ B4GB6 → C4GB5 → C6G95 → B5GA6 ⮌
61 cycle 74,596×(fixed) (max) 1 node ⮎ D91E74 ⮌
73 cycles227,895×2 nodes⮎ C93GC75 → D74GB94 ⮌
12,823×(max) 4 nodes⮎ B72GD96 → E73GC93 → DB4GB54 → C95GA75 ⮌
4,422×2 nodes⮎ D92GD74 → E95GA73 ⮌
83 cycles550,759×4 nodes⮎ 951GGEB8 → FB61EA52 → EC63CA43 → B983C876 ⮌
160,247×3 nodes⮎ D91GGE74 → FC73C942 → D981E874 ⮌
24,448×(max) 5 nodes⮎ A940FC77 → F831ED82 → EC9GG643 → DC82D844 → B97GG876 ⮌
93 cycles1,671,814×(max) 7 nodes⮎ C963GCA75 → D762GDA94 → E972GD973 → EB61GEA53 → FB94GB752 → EB63GCA53 → DB74GB954 ⮌
347,477×6 nodes⮎ C962GDA75 → E862GDA83 → EB71GE953 → FB93GC752 → EC73GC943 → DB84GB854 ⮌
23,667×(fixed) 1 node ⮎ EB82GD853 ⮌
101 cycle 5,311,718×(max) 24 nodes⮎ 6441GGECCB → FCA60FA642 → FD843CC832 → DA97GG8764 → CA630FDA65 → FA743CC962 → D9841EC874 → D981GGE874 → FC750FB942 → FD861EA832 → ECA3GGC643 → DDA61EA634 → DA943CC764 → A8841EC887 → D82GGGGD84 → EC87GG8843 → DC73GGC944 → DC952DB744 → B9861EA876 → D541GGECB4 → FCA80F8642 → FD83GGC832 → EDC53CB433 → BA985A8766 ⮌
112 cycles8,533,747×4 nodes⮎ EB851GEB853 → FB962GDA752 → ED852GDB833 → EBA82GD8653 ⮌
4,504,131×(max) 18 nodes⮎ D9740GFC974 → GB951GEB751 → FF963GCA712 → FDC62GDA432 → EDA95GA7633 → DB842GDC854 → E9972GD9773 → EB621GEEA53 → FCB94GB7542 → EB863GCA853 → DB751GEB954 → FA863GCA862 → EC641GECA43 → FBA85GA8652 → EA641GECA63 → FBA63GCA652 → EC753GCB943 → DB873GC9854 ⮌
121 cycle 30,421,738×(max) 31 nodes⮎ 9842GGGGDC88 → EC8852DB8843 → CA85GGGGA865 → BBA83GGC8656 → DB6531EDBA54 → DA9663CAA764 → A84441ECCC87 → D8882GGD8884 → EC54GGGGBB43 → DCCB30FD5444 → FA9885A88762 → D541GGGGECB4 → FCCB30FD5442 → FDA885A88632 → DA53GGGGCB64 → DCBA30FD6544 → FA9863CA8762 → D9441GGECC74 → FCA952DB7642 → DB8641ECA854 → D9863GGCA874 → DC7520FEB944 → FC9861EA8742 → EC841GGEC843 → FDAA43CC6632 → DA9843CC8764 → A8841GGEC887 → FC741GGEC942 → FEBA52DB6522 → DCB663CAA544 → A88643CCA887 ⮌
132 cycles57,156,872×4 nodes⮎ EBA851GEB8653 → FB9651GEBA752 → FD9652GDBA732 → EDA852GDB8633 ⮌
10,707,026×(max) 9 nodes⮎ EB8531GEDB853 → FBB862GDA8552 → ED8651GEBA833 → FBB851GEB8552 → FD9662GDAA732 → EDA742GDC9633 → EBA962GDA7653 → EB8542GDCB853 → EB9762GDA9753 ⮌
142 cycles145,345,618×(max) 32 nodes⮎ A8841GGGGEC887 → FC98641ECA8742 → EC8841GGEC8843 → FDAA43GGCC6632 → EDC965GGAA7433 → DDA8630FDA8634 → FAA943GGCC7662 → EDB6630FDAA533 → FBAA643CCA6652 → D986443CCCA874 → A88841GGEC8887 → FC741GGGGEC942 → FECC84GGB84422 → EEBA842DC86523 → CCA863GGCA8645 → DC76621EEAA944 → DC98441ECC8744 → D98881GGE88874 → FC750GGGGFB942 → GECB860FA85421 → GEC863GGCA8421 → FEDA641ECA6322 → ECCA843CC86443 → B98883GGC88876 → DA530GGGGFDB64 → GDCB931ED75431 → FDAA861EA86632 → ECA443GGCCC643 → DDA8861EA88634 → DA943GGGGCC764 → DCCA631EDA6444 → DA98843CC88764 ⮌
77,040×(fixed) 1 node ⮎ DC9753GGCB9744 ⮌
153 cycles297,839,232×(fixed) 1 node ⮎ FDB8651GEBA8532 ⮌
2,281,494×(max) 2 nodes⮎ FDB8641GECA8532 → FDB9751GEB97532 ⮌
419,452×(fixed) 1 node ⮎ FDB9741GEC97532 ⮌
164 cycles386,284,512×9 nodes⮎ D981GGGGGGGGE874 → FC988731ED988742 → ECA821GGGGEE8643 → FEDC8661EAA84322 → ECCA843GGCC86443 → DDA88641ECA88634 → DA9843GGGGCC8764 → DCCA6440FCCA6444 → F9888843CC888872 ⮌
203,856,795×(max) 16 nodes⮎ A86421GGGGEECA87 → FECA763GGCA96422 → EECA6630FDAA6423 → FCBA8443CCC86542 → D988863GGCA88874 → DC7520GGGGFEB944 → GECCA740FC964421 → GEC88841EC888421 → FDC87GGGGGG88432 → EDC98870F9887433 → FBA821GGGGEE8652 → FEEB9660FAA75222 → FDCC6441ECCA4432 → ECA88883C8888643 → B983GGGGGGGGC876 → DA988753CB988764 ⮌
7,006,983×5 nodes⮎ DDA650GGGGFBA634 → GDCB9730FD975431 → GEAA8621EEA86621 → FDCC443GGCCC4432 → EDC9887GG8887433 ⮌
3,932,083×11 nodes⮎ A8643GGGGGGCCA87 → DCA98821EE887644 → DC9841GGGGEC8744 → FCCC7542DCB94442 → DB888861EA888854 → D963GGGGGGGGCA74 → DCA97642DCA97644 → B9884421EECC8876 → DC8851GGGGEB8844 → FCCB6542DCBA5442 → DB888663CAA88854 ⮌
176 cycles491,399,653×(max) 18 nodes⮎ EBA74320GFEDC9653 → GDBB9752GDB975531 → FEA86641GECAA8622 → FDCA6441GECCA6432 → FDB98863GCA887532 → ECA7530GGGFDB9643 → GDDB9751GEB975331 → FFBA8641GECA86512 → FEDA7541GECB96322 → FDCB9752GDB975432 → EDA97641GECA97633 → FBB96431GEDCA7552 → FDB97652GDBA97532 → EDA86531GEDBA8633 → FBBA8541GECB86552 → FDA76651GEBAA9632 → FDB85442GDCCB8532 → EDA98762GDA987633 ⮌
345,716,847×4 nodes⮎ FDB86531GEDBA8532 → FDBA8651GEBA86532 → FDB86541GECBA8532 → FDB97651GEBA97532 ⮌
303,879,295×7 nodes⮎ EDA85431GEDCB8633 → FBBA9751GEB976552 → FD966531GEDBAA732 → FDBA8542GDCB86532 → EDA97651GEBA97633 → FBB85431GEDCB8552 → FDB97662GDAA97532 ⮌
23,066,465×4 nodes⮎ FDB97531GEDB97532 → FDBA8641GECA86532 → FDB97541GECB97532 → FDB97641GECA97532 ⮌
1,722,105×2 nodes⮎ FFCB9740GFC975412 → GEDB8741GEC985321 ⮌
1,018,728×2 nodes⮎ FFCB8640GFCA85412 → GEDB8751GEB985321 ⮌
184 cycles2,170,395,426×(max) 79 nodes⮎ 644441GGGGGGECCCCB → FCCCCA2GGGGD644442 → EECCB961GGEA754423 → FEBAA7640FCA966522 → FDC864441ECCCA8432 → ECA88883GGC8888643 → DDA641GGGGGGECA634 → FDCCAA430FDC664432 → FDAA88843CC8886632 → DA9843GGGGGGCC8764 → DCCA98531EDB876444 → DA988641GGECA88764 → FCA76320GGFEDA9642 → GEDCA7630FDA964321 → GECAA8441ECC866421 → FDC88843GGCC888432 → EDC9843GGGGCC87433 → DDDCA6442DCCA64334 → BAA988843CC8887666 → 985441GGGGGGECCB88 → FCCB88630FDA885442 → FDA8863GGGGCA88632 → EDDA95421EECB76333 → DCBAA8641ECA866544 → D9886443GGCCCA8874 → DC986520GGFEBA8744 → GEBA86420FECA86521 → GECC8643GGCCA84421 → FEDA88641ECA886322 → ECCA843GGGGCC86443 → DDCCA6441ECCA64434 → DA9888843CC8888764 → A8841GGGGGGGGEC887 → FC9888861EA8888742 → EC841GGGGGGGGEC843 → FDCC8843GGCC884432 → EDC98843GGCC887433 → DDB98540GGFCB87534 → GDB987430FDC987531 → GEAA8621GGEEA86621 → FFEC88421EEC884212 → EECCC87GGGG8844423 → EDCCA7443CCC964433 → BA9888841EC8888766 → D8541GGGGGGGGECB84 → FCCB88540FCB885442 → FD88865GGGGAA88832 → EDBA7521GGEEB96533 → FEBB98540FCB875522 → FDC86661GGEAAA8432 → FECA76421EECA96422 → ECCC88441ECC884443 → DB88887GGGG8888854 → CB9852GGGGGGDB8755 → EBBB9852GGDB875553 → ED9866430FDCAA8733 → FBAA8441GGECC86652 → FEBA76521EEBA96522 → ECCC66441ECCAA4443 → DB8888843CC8888854 → A885GGGGGGGGGGA887 → B9888865GGAA888876 → BA5320GGGGGGFEDB66 → GEDBAA531EDB665321 → FDCAA6643CCAA66432 → DA9884443CCCC88764 → A888841GGGGEC88887 → FC98641GGGGECA8742 → FECC97440FCC974422 → FDC888821EE8888432 → ECCA7GGGGGGGG86443 → DCCA98641ECA876444 → D9888441GGECC88874 → FCA9540GGGGFCB7642 → GECCA9530FDB764421 → GECA88641ECA886421 → FDC8843GGGGCC88432 → EDDCB5443CCCB54333 → BAA988865AA8887666 ⮌
32,943,057×5 nodes⮎ CA99520GGGGFEB7765 → GEBB97520FEB975521 → GECC66621EEAAA4421 → FDCC88443CCC884432 → DA98887GGGG8888764 ⮌
594,994×2 nodes⮎ DCB84421GGEECC8544 → FEAA98742DC9876622 ⮌
27,936×(fixed) 1 node ⮎ EEBB8832GGDD885523 ⮌
196 cycles1,231,561,993×(max) 11 nodes⮎ EDA987651GEBA987633 → FBB854320GFEDCB8552 → GDDB97662GDAA975331 → FEAA85431GEDCB86622 → FDCB97541GECB975432 → FDB987641GECA987532 → FDB975320GFEDB97532 → GDDBA8641GECA865331 → FFBA97541GECB976512 → FEDA76531GEDBA96322 → FDCBA8542GDCB865432 ⮌
1,125,204,095×4 nodes⮎ FDB976531GEDBA97532 → FDBA86531GEDBA86532 → FDBA86541GECBA86532 → FDB976541GECBA97532 ⮌
983,005,749×2 nodes⮎ FDB865431GEDCBA8532 → FDBA97651GEBA976532 ⮌
653,559,359×2 nodes⮎ FDB975431GEDCB97532 → FDBA97641GECA976532 ⮌
37,177,278×4 nodes⮎ FFCB97640GFCA975412 → GEDB87531GEDB985321 → FFCBA8640GFCA865412 → GEDB87541GECB985321 ⮌
29,420,459×5 nodes⮎ EBA85320GGGFEDB8653 → GEDC99732GDD9774321 → FECAA9521GEEB766422 → FDCCA7542GDCB964432 → EDA988752GDB9887633 ⮌
204 cycles3,692,308,954×(max) 37 nodes⮎ A885GGGGGGGGGGGGA887 → B9888865GGGGAA888876 → BAA93220GGGGFEED7666 → GEED98861GGEA8873221 → FFECB8620GGFEA854212 → GFDDDA9631EDA7633311 → FEDAAAA441ECC6666322 → ECCA884443CCCC886443 → B9888883GGGGC8888876 → DA98430GGGGGGFDC8764 → GDCCA97541ECB9764431 → FDA8886421EECA888632 → ECCA843GGGGGGCC86443 → DDCCCA641GGECA644434 → FDA998865GGAA8877632 → EDA743310GGFFDDC9633 → GFCCBA9750FB97654411 → GEE8866421EECAA88221 → FDCCC843GGGGCC844432 → EDDCB9843GGCC8754333 → DDBA987530FDB9876534 → FAA966421GGEECAA7662 → FEDA864430FDCCA86322 → FDCAA8843GGCC8866432 → EDC986621GGEEAA87433 → FEBBA76320FEDA965522 → FDCCA66441ECCAA64432 → ECA8888443CCC8888643 → B98883GGGGGGGGC88876 → DA98888841EC88888764 → D9841GGGGGGGGGGEC874 → FCC9887431EDC9887442 → ECA88821GGGGEE888643 → FEDC86641GGECAA84322 → FEDBA96621EEAA765322 → ECCCA64441ECCCA64443 → DB88888843CC88888854 ⮌
2,939,185,515×17 nodes⮎ DDA888641GGECA888634 → FDA97621GGGGEEA97632 → FEED987610FFA9873222 → FEDCCA421GGEEC644322 → FEDCBA9861EA87654322 → ECCA86441GGECCA86443 → FDAA886621EEAA886632 → ECCA4443GGGGCCCC6443 → DDCCA8861GGEA8864434 → FDA996621GGEEAA77632 → FEDB87432GGDDC985322 → EEDBA98530FDB8765323 → FCBAA6641GGECAA66542 → FEBA76543GGCCBA96522 → EECA775530FDBB996423 → FCBA866421EECAA86542 → ECC886443GGCCCA88443 ⮌
603,179,673×20 nodes⮎ DA9843GGGGGGGGCC8764 → DCCA98872GGD98876444 → EC9965310GGFFDBA7743 → GFCCA8642GGDCA864411 → FFEB986621EEAA875212 → EECCC6441GGECCA44423 → FEBAA88861EA88866522 → ECC6443GGGGGGCCCA443 → DDCCCC81GGGGE8444434 → FDCCA9943GGCC7764432 → EDC988652GGDBA887433 → EDB986420GGFECA87533 → GECBA86420FECA865421 → GECC88643GGCCA884421 → FEDA88641GGECA886322 → FEDBA7621GGEEA965322 → FEDCB97530FDB9754322 → FDCAA86621EEAA866432 → ECCA84443GGCCCC86443 → DDA8888641ECA8888634 ⮌
73,197,951×3 nodes⮎ ECCCA8861GGEA8864443 → FDAA86621GGEEAA86632 → FEDB874421EECC985322 ⮌
21+---Not showing digit sets 21+ due to verbosity.