Base 19: 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 144×(max) 2 nodes⮎ 3F → B7 ⮌
31 cycle 1,311×(max) 2 nodes⮎ 8IA → 9I9 ⮌
44 cycles1,905×(max) 9 nodes⮎ 74DC → 94DA → 90HA → H0H2 → HE32 → FA74 → B2F8 → D2F6 → D6B6 ⮌
1,821×(max) 9 nodes⮎ 30HG → HC52 → F6B4 → B4D8 → 92FA → D0H6 → H6B2 → F4D4 → B898 ⮌
1,797×(max) 9 nodes⮎ 50HE → H892 → F0H4 → HA72 → F2F4 → DA76 → 72FC → D4D6 → 96BA ⮌
1,773×(max) 9 nodes⮎ 52FE → D896 → 70HC → H4D2 → F894 → B0H8 → H2F2 → FC54 → B6B8 ⮌
52 cycles23,279×3 nodes⮎ C4ID7 → E5IC5 → D8I96 ⮌
10,351×(max) 4 nodes⮎ C5IC7 → D4ID6 → E6IB5 → D7IA6 ⮌
65 cycles59,413×5 nodes⮎ B51GD8 → F82FA4 → DB1G76 → F73EB4 → CA3E87 ⮌
43,788×2 nodes⮎ F40HE4 → HB9872 ⮌
12,595×(max) 6 nodes⮎ 531GFE → FC8964 → B60HC8 → H62FC2 → FD5C54 → B86BA8 ⮌
10,271×4 nodes⮎ 72IIFC → GB2F73 → EC3E65 → B95C98 ⮌
8,510×4 nodes⮎ 863ECB → B62FC8 → D62FC6 → D75CB6 ⮌
71 cycle 480,681×(max) 14 nodes⮎ E83IEA5 → F95IC94 → EA2IF85 → GA5IC83 → FB3IE74 → FB6IB74 → E93IE95 → F94ID94 → EB3IE75 → F96IB94 → E91IG95 → HB4ID72 → GD5IC53 → FB7IA74 ⮌
83 cycles839,012×(max) 5 nodes⮎ B651GDC8 → F862FCA4 → DB61GC76 → F763ECB4 → CA63EC87 ⮌
651,292×(max) 5 nodes⮎ CA41GE87 → FA51GD84 → FB81GA74 → FB41GE74 → FBA3E874 ⮌
71,952×4 nodes⮎ 8663ECCB → B662FCC8 → D662FCC6 → D765CCB6 ⮌
92 cycles4,601,070×(max) 2 nodes⮎ FB52IFD74 → GBA5IC873 ⮌
85,736×(fixed) 1 node ⮎ FB73IEB74 ⮌
105 cycles7,466,825×5 nodes⮎ CA641GEC87 → FA651GDC84 → FB861GCA74 → FB641GEC74 → FBA63EC874 ⮌
3,710,718×(fixed) 1 node ⮎ FBA41GE874 ⮌
1,653,290×5 nodes⮎ B6651GDCC8 → F8662FCCA4 → DB661GCC76 → F7663ECCB4 → CA663ECC87 ⮌
271,174×(max) 10 nodes⮎ B761IIGCB8 → HC93IIE962 → GFB52FD733 → ECC83EA665 → B9661GCC98 → F662IIFCC4 → GE98II9943 → FE84IIDA44 → EEB62FC745 → DA963EC986 ⮌
21,084×4 nodes⮎ 86663ECCCB → B6662FCCC8 → D6662FCCC6 → D7665CCCB6 ⮌
112 cycles22,997,597×5 nodes⮎ FB951IGD974 → HCA61IGC862 → HFA63IEC832 → GEC83IEA643 → FDA83IEA854 ⮌
11,599,674×(max) 8 nodes⮎ FC861IGCA64 → HC963IEC962 → GE862IFCA43 → GDB83IEA753 → FD962IFC954 → GBA72IFB873 → GD842IFEA53 → GDB94ID9753 ⮌
126 cycles41,838,443×(fixed) 1 node ⮎ FBA641GEC874 ⮌
21,598,028×5 nodes⮎ CA6641GECC87 → FA6651GDCC84 → FB8661GCCA74 → FB6641GECC74 → FBA663ECC874 ⮌
19,543,331×3 nodes⮎ FBA421GGE874 → FEBA41GE8744 → FBAA41GE8874 ⮌
2,913,702×5 nodes⮎ B66651GDCCC8 → F86662FCCCA4 → DB6661GCCC76 → F76663ECCCB4 → CA6663ECCC87 ⮌
562,328×(max) 9 nodes⮎ ECCA61GC8665 → F96661GCCC94 → FB665IICCC74 → ED9650HDC955 → H9885IICAA92 → GD9410HHE953 → HGDA7IIA8522 → GGC94IID9623 → GFCA42FE8633 ⮌
37,374×4 nodes⮎ 866663ECCCCB → B66662FCCCC8 → D66662FCCCC6 → D76665CCCCB6 ⮌
132 cycles205,813,452×(max) 21 nodes⮎ FD9751IGDB954 → HCA861IGCA862 → HFA641IGEC832 → HFDB83IEA7532 → GEC962IFC9643 → GDB862IFCA753 → GDA752IFDB853 → GDA862IFCA853 → GDA741IGEB853 → HDC962IFC9652 → GFA762IFCB833 → GDC952IFD9653 → GDA872IFBA853 → GDA631IGFC853 → HDDA73IEB8552 → GE9862IFCA943 → GDB840IHEA753 → IEC962IFC9641 → HGB862IFCA722 → GFE952IFD9433 → GDCB93IE97653 ⮌
439,604×3 nodes⮎ GFC830IHFA633 → IEDC93IE96541 → HFA972IFB9832 ⮌
148 cycles186,572,141×3 nodes⮎ FBA6421GGEC874 → FEBA641GEC8744 → FBAA641GEC8874 ⮌
162,172,688×(fixed) 1 node ⮎ FBA6641GECC874 ⮌
51,679,864×(max) 5 nodes⮎ CA66641GECCC87 → FA66651GDCCC84 → FB86661GCCCA74 → FB66641GECCC74 → FBA6663ECCC874 ⮌
37,845,197×3 nodes⮎ FBA4221GGGE874 → FEEBA41GE87444 → FBAAA41GE88874 ⮌
28,269,656×3 nodes⮎ FBAA421GGE8874 → FEBA421GGE8744 → FEBAA41GE88744 ⮌
4,814,623×(max) 5 nodes⮎ B666651GDCCCC8 → F866662FCCCCA4 → DB66661GCCCC76 → F766663ECCCCB4 → CA66663ECCCC87 ⮌
48,100×4 nodes⮎ 8666663ECCCCCB → B666662FCCCCC8 → D666662FCCCCC6 → D766665CCCCCB6 ⮌
33,312×(fixed) 1 node ⮎ FEB773IIEBB744 ⮌
153 cycles823,555,820×(max) 63 nodes⮎ FD97531IGFDB954 → HDBA861IGCA8752 → HFB7531IGFDB732 → HFDCA63IEC86532 → GEC9763IECB9643 → FDA8651IGDCA854 → HCA8741IGEBA862 → HFC8531IGFDA632 → HFDCA73IEB86532 → GEC9752IFDB9643 → GDB9751IGDB9753 → HDB8641IGECA752 → HFC9752IFDB9632 → GFCA751IGDB8633 → HDDA752IFDB8552 → GFA8862IFCAA833 → GDC9421IGGE9653 → HEDC972IFB96542 → GFB9751IGDB9733 → HDDA641IGEC8552 → HFC9873IEBA9632 → GEC8530IHFDA643 → IEDB973IEB97541 → HFA9641IGEC9832 → HFDB840IHEA7532 → IFEB962IFC97431 → HGCB851IGDA7622 → HFEB752IFDB7432 → GFCB963IEC97633 → FDC8651IGDCA654 → HCA8763IECBA862 → GE86531IGFDCA43 → HDDB973IEB97552 → GE98641IGECA943 → HDCA840IHEA8652 → IFD9741IGEB9531 → HHDB961IGC97512 → HGFB751IGDB7322 → HFEDA63IEC85432 → GECA973IEB98643 → FDA8530IHFDA854 → IEBA851IGDA8741 → HHC9631IGFC9612 → HGFD962IFC95322 → GFECA72IFB86433 → GDCB852IFDA7653 → GDA8752IFDBA853 → GDA8631IGFCA853 → HDDA741IGEB8552 → HFC9862IFCA9632 → GFC9640IHEC9633 → IEDB862IFCA7541 → HGB9752IFDB9722 → GFEA641IGEC8433 → HDDBA83IEA87552 → GE98631IGFCA943 → HDDB840IHEA7552 → IFD9862IFCA9531 → HGCA740IHEB8622 → IFFC852IFDA6331 → HGCCA73IEB86622 → GFD8652IFDCA533 → GDCA873IEBA8653 ⮌
211,913,244×22 nodes⮎ GDA7651IGDCB853 → HDB8752IFDBA752 → GFA8642IFECA833 → GDCB841IGEA7653 → HDC9752IFDB9652 → GFA8751IGDBA833 → HDDA631IGFC8552 → HFDA873IEBA8532 → GEC9631IGFC9643 → HDDB862IFCA7552 → GFA8752IFDBA833 → GDCA631IGFC8653 → HDDA763IECB8552 → GE98752IFDBA943 → GDB9630IHFC9753 → IEDA751IGDB8541 → HHC9862IFCA9612 → HFF9640IHEC9332 → IFECB82IFA76431 → HGCB852IFDA7622 → GFEA752IFDB8433 → GDCB962IFC97653 ⮌
1,689,237×(fixed) 1 node ⮎ HFDA851IGDA8532 ⮌
1611 cycles816,826,911×3 nodes⮎ FBA66421GGECC874 → FEBA6641GECC8744 → FBAA6641GECC8874 ⮌
379,697,227×3 nodes⮎ FBAA6421GGEC8874 → FEBA6421GGEC8744 → FEBAA641GEC88744 ⮌
378,521,926×(fixed) 1 node ⮎ FBA66641GECCC874 ⮌
302,223,832×3 nodes⮎ FBA64221GGGEC874 → FEEBA641GEC87444 → FBAAA641GEC88874 ⮌
140,306,386×(max) 5 nodes⮎ CA666641GECCCC87 → FA666651GDCCCC84 → FB866661GCCCCA74 → FB666641GECCCC74 → FBA66663ECCCC874 ⮌
59,417,377×3 nodes⮎ FBAAA421GGE88874 → FEBA4221GGGE8744 → FEEBAA41GE887444 ⮌
54,260,111×3 nodes⮎ FBAA4221GGGE8874 → FEEBA421GGE87444 → FEBAAA41GE888744 ⮌
52,787,127×3 nodes⮎ FBA42221GGGGE874 → FEEEBA41GE874444 → FBAAAA41GE888874 ⮌
13,647,687×(fixed) 1 node ⮎ FEBAA421GGE88744 ⮌
6,203,454×(max) 5 nodes⮎ B6666651GDCCCCC8 → F8666662FCCCCCA4 → DB666661GCCCCC76 → F7666663ECCCCCB4 → CA666663ECCCCC87 ⮌
69,373×4 nodes⮎ 86666663ECCCCCCB → B6666662FCCCCCC8 → D6666662FCCCCCC6 → D7666665CCCCCCB6 ⮌
174 cycles3,906,769,576×(max) 31 nodes⮎ FDC97541IGEDB9654 → HCB98751IGDBA9762 → HFB75430IHFEDB732 → IFECB963IEC976431 → HFCA8651IGDCA8632 → HFDA7641IGECB8532 → HFDB9752IFDB97532 → GFCA8641IGECA8633 → HDDB8641IGECA7552 → HFC98752IFDBA9632 → GFCA7530IHFDB8633 → IEDCA752IFDB86541 → HGB98752IFDBA9722 → GFEA6430IHFEC8433 → IEDCBA83IEA876541 → HFA97531IGFDB9832 → HFDCA630IHFC86532 → IFECA763IECB86431 → HFCA8652IFDCA8632 → GFCA7641IGECB8633 → HDDB8652IFDCA7552 → GFA88752IFDBAA833 → GDCA6321IGGFC8653 → HEDDA763IECB85542 → GEA98752IFDBA9843 → GDB96320IHGFC9753 → IFDDA751IGDB85531 → HHDA8862IFCAA8512 → HFFA7421IGGEB8332 → HFEDCB72IFB765432 → GFCB9753IEDB97633 ⮌
479,462,248×5 nodes⮎ GEC96430IHFEC9643 → IEDBA862IFCA87541 → HGB97531IGFDB9722 → HFEDA641IGEC85432 → HFDBA973IEB987532 ⮌
149,388,246×4 nodes⮎ HFDA8641IGECA8532 → HFDB9741IGEB97532 → HFDB9641IGEC97532 → HFDB9751IGDB97532 ⮌
1,947,561×2 nodes⮎ HHEDA850IHDA85412 → IGFD9851IGDA95321 ⮌
1817 cycles2,294,297,992×3 nodes⮎ FBA666421GGECCC874 → FEBA66641GECCC8744 → FBAA66641GECCC8874 ⮌
1,476,060,977×3 nodes⮎ FBA664221GGGECC874 → FEEBA6641GECC87444 → FBAAA6641GECC88874 ⮌
1,333,759,786×3 nodes⮎ FBAA66421GGECC8874 → FEBA66421GGECC8744 → FEBAA6641GECC88744 ⮌
1,082,075,756×(fixed) 1 node ⮎ FBA666641GECCCC874 ⮌
803,308,420×3 nodes⮎ FBAAA6421GGEC88874 → FEBA64221GGGEC8744 → FEEBAA641GEC887444 ⮌
714,782,528×3 nodes⮎ FBA642221GGGGEC874 → FEEEBA641GEC874444 → FBAAAA641GEC888874 ⮌
512,090,345×3 nodes⮎ FBAA64221GGGEC8874 → FEEBA6421GGEC87444 → FEBAAA641GEC888744 ⮌
246,417,609×(max) 5 nodes⮎ CA6666641GECCCCC87 → FA6666651GDCCCCC84 → FB8666661GCCCCCA74 → FB6666641GECCCCC74 → FBA666663ECCCCC874 ⮌
172,933,764×(fixed) 1 node ⮎ FEBAA6421GGEC88744 ⮌
137,472,631×3 nodes⮎ FBAAA4221GGGE88874 → FEEBA4221GGGE87444 → FEEBAAA41GE8887444 ⮌
83,610,760×3 nodes⮎ FEBAA4221GGGE88744 → FEEBAA421GGE887444 → FEBAAA421GGE888744 ⮌
82,267,491×3 nodes⮎ FBAA42221GGGGE8874 → FEEEBA421GGE874444 → FEBAAAA41GE8888744 ⮌
67,466,958×3 nodes⮎ FBAAAA421GGE888874 → FEBA42221GGGGE8744 → FEEEBAA41GE8874444 ⮌
59,071,172×3 nodes⮎ FBA422221GGGGGE874 → FEEEEBA41GE8744444 → FBAAAAA41GE8888874 ⮌
9,405,604×(max) 5 nodes⮎ B66666651GDCCCCCC8 → F86666662FCCCCCCA4 → DB6666661GCCCCCC76 → F76666663ECCCCCCB4 → CA6666663ECCCCCC87 ⮌
89,388×4 nodes⮎ 866666663ECCCCCCCB → B66666662FCCCCCCC8 → D66666662FCCCCCCC6 → D76666665CCCCCCCB6 ⮌
24,100×(fixed) 1 node ⮎ FFBB7743IIEEBB7734 ⮌
19+---Not showing digit sets 19+ due to verbosity.