Base 15: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDE

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--
20 cycles--
31 cycle 2 nodes⮎ 6E8 → 7E7 ⮌
47 cycles4 nodes⮎ 72B8 → 90D6 → D2B2 → B854 ⮌
51 cycle (fixed) 1 node ⮎ A4E95 ⮌
62 cycles9 nodes⮎ 41EECB → DA0D42 → DB5832 → B82B64 → 971C76 → B2EEB4 → C9EE43 → BA2B44 → 975876 ⮌
72 cycles10 nodes⮎ B70ED74 → E93EA51 → DB4E932 → CA6E743 → B83EA64 → B73EA74 → B72EB74 → C73EA73 → B92EB54 → C75E873 ⮌
84 cycles22 nodes⮎ 861EEC87 → D84EE962 → CA70D743 → D95EE852 → C980D653 → D941CA52 → CA63A843 → 9761C876 → B31EECB4 → DB7EE632 → CB73A733 → 986EE766 → 8830DB67 → D820DC62 → DBA1C432 → CA858643 → 9631CB86 → B831CB64 → B871C764 → B71EEC74 → DA53A942 → B763A874 ⮌
93 cycles8 nodes⮎ A742EBA75 → C752EB973 → C961EC853 → D972EB752 → CB61EC833 → D994E9552 → C943EAA53 → B964E9854 ⮌
103 cycles6 nodes⮎ B761EEC874 → DA640DA842 → DB661C8832 → CA821CC643 → BA961C8544 → B7641CA874 ⮌
114 cycles11 nodes⮎ B9641ECA854 → D8752EB9762 → CB630EDB833 → EA984E96541 → DA642EBA842 → CB763EA8733 → B9840EDA654 → E9752EB9751 → DC641ECA822 → DBA83EA6432 → CA863EA8643 ⮌
122 cycles19 nodes⮎ 764321CCBA88 → BA8620DC8644 → DA7621CC8742 → CAA61EEC8443 → DB8841CA6632 → CA8621CC8643 → BA9621CC8544 → BA7641CA8744 → B7661EEC8874 → DA6510DD9842 → DCB641CA8322 → CAA861C86443 → B96621CC8854 → BA7421CCA744 → BA765EE88744 → AA6410DDA845 → DC6651C98822 → CAA421CCA443 → BA9665888544 ⮌
132 cycles4 nodes⮎ CB8641ECA8633 → D99741ECA7552 → DB8541ECA9632 → DB9752EB97532 ⮌
144 cycles7 nodes⮎ 9666321CCB8886 → BA83221CCCB644 → BAA8761C876444 → B76621EECC8874 → DC86510DD98622 → DCBA421CCA4322 → CAAA8658864443 ⮌
157 cycles33 nodes⮎ CB75430EDBA9733 → EA98751EC976541 → DD85430EDBA9612 → ECBA752EB974321 → DCA8751EC976422 → DBA8530EDB96432 → EBA8752EB976431 → DC87530EDB97622 → EBB9630EDB85331 → EDA8862EB866411 → DDB7421ECCA7312 → DCBA972EB754322 → CBA8751EC976433 → D997530EDB97552 → EBA6441ECAA8431 → DD97663EA887512 → DBA5320EDCB9432 → EBB9874E9765331 → DB87430EDBA7632 → EBA8740EDA76431 → EDA7640EDA87411 → EDC9640EDA85211 → EDCB852EB963211 → DDBA862EB864312 → DBB8741ECA76332 → DB98740EDA76532 → EBA7530EDB97431 → EDA8751EC976411 → DDC8530EDB96212 → ECBB962EB853321 → DCA8862EB866422 → CBA7421ECCA7433 → DA99762EB875542 ⮌
166 cycles6 nodes⮎ BA76661EEC888744 → DA854210DDCA9642 → DCBA6641CA884322 → CAA86621CC886443 → BA966221CCC88544 → BAA76421CCA87444 ⮌
175 cycles11 nodes⮎ CB876531ECB987633 → D9986320EDCB86552 → EBB96431ECBA85331 → DD988752EB9766512 → DBB64320EDCBA8332 → EBB98873EA7665331 → DB885320EDCB96632 → EBB98631ECB865331 → DD988631ECB866512 → DCB96321ECCB85322 → DBAA9862EB8654432 ⮌
185 cycles10 nodes⮎ AA7542210DDCCA9745 → DCAA6653EEA9884422 → CCA86542EEBA986423 → CC987542EEBA976523 → CC9865320DCB986523 → DAA984421CCAA65442 → CAA666641CA8888443 → B96662221CCCC88854 → BAAA74221CCCA74444 → BAA76665EE88887444 ⮌
194 cycles18 nodes⮎ CB8754320EDCBA97633 → EB9987530EDB9765531 → EDA864430EDBAA86411 → EDCA76641ECA8874211 → DDCA86420EDCA864212 → ECBBA8641ECA8643321 → DDA987641ECA8765412 → DCB865320EDCB986322 → EBBA98631ECB8654331 → DD9887531ECB9766512 → DCB964320EDCBA85322 → EBBA98752EB97654331 → DC8875430EDBA976622 → EBB975320EDCB975331 → EDB988641ECA8665311 → DDC975321ECCB975212 → DCBAA9641ECA8544322 → DBA976652EB98875432 ⮌
205 cycles27 nodes⮎ BAA7664221CCCA887444 → BAA766621EECC8887444 → DC88744210DDCAA76622 → DCBAA6621EECC8844322 → DCBA98743EEAA7654322 → CCA9765420DCA9875423 → DAA966441EECAA885442 → DC9866542EEBA9886522 → CCB865331EECBB986323 → DC9998652EEB98655522 → CCB764432EEBBAA87323 → CC99877430DBA7765523 → DA986441EEEECAA86542 → DCAA974420DCAA754422 → DBAA66663EEA88884432 → CBA764421EECCAA87433 → DC99876430DBA8765522 → DBA864421EECCAA86432 → DCB987643EEAA8765322 → CCA9754310DDBA975423 → DCA986643EEAA8865422 → CCA865431EECBA986423 → DC9987542EEBA9765522 → CCB8654320DCBA986323 → DAA9886421CCA8665442 → CAA6664221CCCA888443 → BAA9666221CCC8885444 ⮌
213 cycles11 nodes⮎ DC88643220EDCCBA86622 → EBBAA97421ECCA7544331 → DDA9876651EC988765412 → DCB8543220EDCCBA96322 → EBBAA98752EB976544331 → DC88765430EDBA9876622 → EBB9753220EDCCB975331 → EDBA988641ECA86654311 → DDC9765321ECCB9875212 → DCBAA96430EDBA8544322 → EBB9876652EB988765331 ⮌
226 cycles16 nodes⮎ BAA76642221CCCCA887444 → BAAA766621EECC88874444 → DC887644210DDCAA876622 → DCBAA66221EECCC8844322 → DCBAA98743EEAA76544322 → CCA97665420DCA98875423 → DAA9664421EECCAA885442 → DCB8866542EEBA98866322 → CCB9764321EECCBA875323 → DCA99976420DCA87555422 → DBAA664441EECAAA884432 → DCA8766643EEAA88876422 → CCA86442210DDCCAA86423 → DCAAA966621CC888544422 → CAAA6664221CCCA8884443 → BAA96666221CCC88885444 ⮌
237 cycles11 nodes⮎ DCB86543220EDCCBA986322 → EBBAA987531ECB976544331 → DD988765430EDBA98766512 → ECBA7543220EDCCBA974321 → EDBAA987651EC9876544311 → DDC97654320EDCBA9875212 → ECBBA975430EDBA97543321 → EDB98876541ECA987665311 → DDC97543220EDCCBA975212 → ECBBAA97541ECA975443321 → DDA98766541ECA988765412 ⮌
249 cycles16 nodes⮎ AA7542222210DDCCCCCA9745 → DCAAAAA6653EEA9884444422 → CCA86666542EEBA988886423 → CC987543221EECCCBA976523 → DCAA99865320DCB986554422 → DBAA86644421CCAAA8864432 → CAA866666221CCC888886443 → BAA966222221CCCCCC885444 → BAAAAA766421CCA887444444 → BA766666621EECC888888744 → DC8854222210DDCCCCA96622 → DCBAAAAA6421CCA844444322 → CAAA86666661C88888864443 → B96662222221CCCCCCC88854 → BAAAAAA74221CCCA74444444 → BAA76666665EE88888887444 ⮌