Base 13: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABC

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 3 nodes⮎ 1B → 93 → 57 ⮌
31 cycle 2 nodes⮎ 5C7 → 6C6 ⮌
43 cycles6 nodes⮎ 30BA → B652 → 90B4 → B472 → 9294 → 7476 ⮌
51 cycle 4 nodes⮎ 83C85 → 92C94 → A4C73 → 95C64 ⮌
61 cycle (fixed) 1 node ⮎ 951A74 ⮌
73 cycles12 nodes⮎ 951CA74 → B63C862 → A81CA43 → B75C652 → A61CA63 → B73C852 → A82C943 → A74C753 → 961CA64 → B62C962 → A92C933 → A75C653 ⮌
82 cycles4 nodes⮎ 641CCA87 → B840B842 → B9438832 → 96538764 ⮌
93 cycles5 nodes⮎ 9620CBA64 → C962C9631 → BA62C9622 → A982C9433 → A764C7653 ⮌
104 cycles9 nodes⮎ 86661A6665 → 92CCCCCC94 → A832CC9943 → A9750B7533 → B7621AA652 → A881CCA443 → B965CC6632 → A962CC9633 → A973299533 ⮌
111 cycle 14 nodes⮎ A8520CBA743 → C9762C96531 → BA640CB8622 → C9961CA6331 → BB762C96512 → B9940CB8332 → C9864C76431 → B9540CB8732 → C9852C97431 → BA652C97622 → A9840CB8433 → C8753C87541 → B9431CA9832 → B9764C76532 ⮌
123 cycles10 nodes⮎ 96543CC88764 → 985320BA9744 → B86541A87642 → A8441CCA8843 → B9663CC86632 → A9831CCA9433 → B97750B75532 → B96221AAA632 → A8885CC64443 → 986431A98644 ⮌
133 cycles10 nodes⮎ A76530CB97653 → C87420CBA8541 → CB9642C986311 → BB9651CA76312 → BA9740CB85322 → C99752C975331 → BA6641CA86622 → B9861CCCA6432 → BA9742C985322 → A98652C976433 ⮌
143 cycles15 nodes⮎ A8441CCCCA8843 → B98861CCA64432 → BA86521AA76422 → A88841CCA84443 → B96643CC886632 → A98521CCAA7433 → BA77640B865522 → B98421CCAA8432 → BA9764CC765322 → AA86410BB86423 → BA8743CC885422 → AA86430B986423 → B87643CC886542 → A974320BA98533 → B876641A866542 ⮌
152 cycles14 nodes⮎ A966530CB976633 → C87640CCCB86541 → CB88621CAA64411 → BBA8641CA864212 → BA98641CA864322 → B987541CA875432 → B975431CA987532 → B976531CA976532 → B976420CBA86532 → C997530CB975331 → CB86641CA866411 → BBA641CCCA86212 → BBA9743C8853212 → B997642C9865332 ⮌
163 cycles11 nodes⮎ 9988621CCAA64434 → BA765521AA776522 → A888221CCAAA4443 → BA87663CC8665422 → AA86320CCBA96423 → CA977631A9655321 → B986621CCAA66432 → BA97631CCA965322 → BA977430B9855322 → B9866421AA866432 → A88643CCCC886443 ⮌
174 cycles23 nodes⮎ A974430CCCB988533 → C9986540CB8764331 → CB865430CB9876411 → CBA85430CB9874211 → CBA97542C98753211 → BB986531CA9764312 → BA976530CB9765322 → C9976420CBA865331 → CB976530CB9765311 → CBA86420CBA864211 → CBA98641CA8643211 → BBA87541CA8754212 → BA986431CA9864322 → B9876541CA8765432 → B9754320CBA987532 → C9976531CA9765331 → BB766420CBA866512 → CA99630CCCB963321 → CBA98732C99543211 → BB986652C97664312 → B996530CCCB976332 → CA988432C99844321 → BA866543C88766422 ⮌
182 cycles12 nodes⮎ 954441CCCCCCA88874 → B8888730CCB9544442 → CA8754430B98875421 → CA8644421AA8886421 → B9884443CC88884432 → A9854443CC88887433 → 997544430B98887534 → B66544421AA8887662 → A884441CCCCA888443 → B988663CCCC8664432 → A99873221AAA954333 → 988766641A86665444 ⮌
192 cycles8 nodes⮎ BA9754320CBA9875322 → C99876531CA97654331 → BB7665320CBA9766512 → CA997420CCCBA853321 → CBAA87641CA86542211 → BBA886430CB98644212 → CA9975441CA88753321 → BB8765431CA98765412 ⮌
205 cycles12 nodes⮎ 98544441CCCCA8888744 → B88865430CCB98764442 → CA87544320BA98875421 → CA88644421AA88864421 → B98844443CC888884432 → A98544443CC888887433 → 9975444430B988887534 → B665444421AA88887662 → A8844441CCCCA8888443 → B9886643CCCC88664432 → A998752221AAAA754333 → 9888766421AA86654444 ⮌
214 cycles18 nodes⮎ BBA754320CCCBA9875212 → CBA9986540CB876433211 → CBA9765430CB987653211 → CBA9765320CBA97653211 → CBA9876420CBA86543211 → CBA9875430CB987543211 → CBA9765431CA987653211 → BBA8765320CBA97654212 → CA99875320CBA97543321 → CB98766531CA976654311 → BBA765320CCCBA9765212 → CBA9985530CB977433211 → CBA9766531CA976653211 → BBA876420CCCBA8654212 → CBA9976521CAA76533211 → BBA8876420CBA86544212 → CA99864430CB988643321 → CB97665441CA887665311 ⮌
224 cycles12 nodes⮎ 985444441CCCCA88888744 → B888654430CCB988764442 → CA875444320BA988875421 → CA886444421AA888864421 → B988444443CC8888884432 → A985444443CC8888887433 → 99754444430B9888887534 → B6654444421AA888887662 → A88444441CCCCA88888443 → B98866443CCCC888664432 → A9987542221AAAA8754333 → 98887664421AA886654444 ⮌
234 cycles15 nodes⮎ BA665320CCCCCCCBA976622 → CAAA9765542C98776532221 → BA888653220CBAA97644422 → C9988754430CB9887544331 → CB866544431CA9888766411 → BBA7544430CCCB988875212 → CBA98765330CB9976543211 → CBA97665320CBA976653211 → CBA9876420CCCBA86543211 → CBBA9866421CAA866432111 → BBAA887541CCCA875442212 → BBA99666330CB9966633212 → CA9976662CCCCC966653321 → BAA99743330CB9998533222 → C9987666652C97666654331 ⮌
243 cycles12 nodes⮎ 9854444441CCCCA888888744 → B8886544430CCB9888764442 → CA8754444320BA9888875421 → CA8864444421AA8888864421 → B9884444443CC88888884432 → A9854444443CC88888887433 → 997544444430B98888887534 → B66544444421AA8888887662 → A884444441CCCCA888888443 → B988664443CCCC8888664432 → A99875442221AAAA88754333 → 988876644421AA8886654444 ⮌
255 cycles8 nodes⮎ BBA76544320CCCBA988765212 → CBA998664320CBA9866433211 → CBA98766541CCCA8766543211 → BBBA86643210CBBA986642112 → CAAA9987541CCCA8754332221 → BBAA87765430CB98765542212 → CA9987543220CBAA987543321 → CB9887665431CA98766544311 ⮌
263 cycles12 nodes⮎ 98544444441CCCCA8888888744 → B88865444430CCB98888764442 → CA87544444320BA98888875421 → CA88644444421AA88888864421 → B98844444443CC888888884432 → A98544444443CC888888887433 → 9975444444430B988888887534 → B665444444421AA88888887662 → A8844444441CCCCA8888888443 → B9886644443CCCC88888664432 → A998754442221AAAA888754333 → 9888766444421AA88886654444 ⮌
276 cycles5 nodes⮎ BBAAA8876530CCCB97654422212 → CBA9997664320CBA98665333211 → CBA987666530CCCB97666543211 → CBBA88644210CCCBBA886442111 → CBBBA99766421CAA86653321111 ⮌
284 cycles12 nodes⮎ 985444444441CCCCA88888888744 → B888654444430CCB988888764442 → CA875444444320BA988888875421 → CA886444444421AA888888864421 → B988444444443CC8888888884432 → A985444444443CC8888888887433 → 99754444444430B9888888887534 → B6654444444421AA888888887662 → A88444444441CCCCA88888888443 → B98866444443CCCC888888664432 → A9987544442221AAAA8888754333 → 98887664444421AA888886654444 ⮌
299 cycles5 nodes⮎ BBAAA88766530CCCB976654422212 → CBA99976643210CBBA98665333211 → CBAA987666530CCCB976665432211 → CBBA987644210CCCBBA8865432111 → CBBBA998665321CAA976643321111 ⮌