Base 9: Cycles Lengths: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
012345678

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)
Nodes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
10 cycles-----------------------------------------------------------------
21 cycle -32×
---------------------------------------------------------------
31 cycle -156×
---------------------------------------------------------------
42 cycles--486×
--------------------------------------------------------------
52 cycles93×
---1,185×
------------------------------------------------------------
61 cycle -------------2,994×
---------------------------------------------------
71 cycle -6,426×
---------------------------------------------------------------
82 cycles200×
--12,661×
-------------------------------------------------------------
92 cycles3,013×
----------21,288×
-----------------------------------------------------
103 cycles441×
--36,148×
7,160×
------------------------------------------------------------
112 cycles216×
----75,357×
-----------------------------------------------------------
123 cycles-112,701×
---13,260×
-----------------------------------------------------------
133 cycles192×
--175,626×
-27,663×
-----------------------------------------------------------
143 cycles4,608×
---------315,153×
------------------------------------------------------
154 cycles508×
-52,473×
349,818×
-87,506×
-----------------------------------------------------------
162 cycles264×
735,198×
---------------------------------------------------------------
174 cycles408,450×
8,012×
----665,104×
----------------------------------------------------------
184 cycles22,701×
----348,611×
--1,190,954×
--------------------------------------------------------
195 cycles63,782×
--2,156,284×
-------------------------------------------------------------
204 cycles1,184×
----22,678×
--------3,084,234×
--------------------------------------------------
216 cycles52,841×
--246,219×
-2,314,027×
1,679,049×
----------------------------------------------------------
225 cycles408×
186,351×
-------5,666,157×
-------------------------------------------------------
239 cycles56,245×
290,085×
394,019×
119,309×
--409,389×
6,619,669×
---------------------------------------------------------
244 cycles21,134×
8,698,985×
---1,798,172×
-----------------------------------------------------------
2515 cycles53,769×
5,127,292×
1,108,412×
1,221,227×
-4,072,037×
1,353,449×
947,961×
---------------------------------------------------------
264 cycles984×
8,370,211×
----------9,785,000×
----------------------------------------------------
2715 cycles118,314×
910,846×
348,582×
1,589,598×
1,381,840×
738,683×
409,389×
947,961×
-----------17,090,598×
---------------------------------------------
285 cycles7,032×
----1,022,355×
------------------------29,230,944×
----------------------------------
2918 cycles86,557×
893,881×
547,667×
850,477×
1,655,760×
738,683×
7,115,941×
26,719,045×
---------------------------------------------------------
305 cycles1,696×
-----18,621,201×
--------------30,280,586×
-------------------------------------------
3119 cycles53,609×
893,881×
988,199×
850,477×
13,724,371×
738,683×
2,638,649×
41,635,870×
---------------------------------------------------------
327 cycles6,862,244×
14,434,970×
--------------------------------55,607,462×
------------------------------
3323 cycles59,797×
893,881×
348,582×
850,477×
13,253,004×
738,683×
2,638,649×
13,851,132×
--------------------62,914,031×
------------------------------------
345 cycles792,204×
--------------------117,237,972×
-------------------------------------------
3530 cycles55,041×
893,881×
348,582×
850,477×
112,344,560×
738,683×
2,638,649×
27,138,631×
---------------------------------------------------------
366 cycles841,156×
--52,547,856×
----123,843,606×
--------------------------------------------------------
3732 cycles60,321×
926,057×
348,582×
25,599,065×
17,380,453×
738,683×
2,638,649×
13,851,132×
---------154,010,244×
-----------------------------------------------
388 cycles743,212×
--8,302,635×
--251,886,959×
----------------------------------------------------------
3932 cycles128,573×
893,881×
348,582×
43,393,842×
17,380,453×
738,683×
2,638,649×
13,851,132×
------59,662,178×
--175,421,513×
-----------------------------------------------
408 cycles736,564×
--8,302,635×
-41,291,458×
221,623,229×
-------------105,395,099×
--------------------------------------------
4134 cycles70,725×
893,881×
348,582×
22,639,105×
17,380,453×
738,683×
2,638,649×
13,851,132×
----6,122,998×
-11,392,037×
-----------------------374,901,812×
--------------------------
4211 cycles752,888×
45,500×
-8,302,635×
--72,353,422×
-200,718,378×
------204,969,840×
-----49,735,978×
-------------------------------------------
4334 cycles64,701×
893,881×
348,582×
22,639,105×
17,380,453×
738,683×
2,638,649×
13,851,132×
------11,392,037×
-----------566,815,818×
--------------------------------------
4411 cycles839,660×
9,697,631×
44,786,963×
8,302,635×
17,033,005×
-12,571,741×
659,306,506×
---------------------------------------------------------
4539 cycles322,377×
893,881×
7,322,643×
22,639,105×
17,380,453×
738,683×
611,654,490×
13,851,132×
---157,472,712×
--11,392,037×
42,655,188×
-------------------------------------------------
4612 cycles756,052×
4,012,308×
7,395,002×
8,302,635×
--12,571,741×
26,886,569×
-----253,315,232×
-------727,226,242×
-------------------------------------------
4742 cycles3,443,253×
243,236,043×
1,477,324×
22,639,105×
102,414,423×
738,683×
147,257,367×
13,851,132×
---48,746,880×
--11,392,037×
---------------622,370,094×
----------------------------------
4814 cycles755,624×
897,611,263×
142,972,052×
8,302,635×
130,671,653×
200,722,529×
12,571,741×
26,886,569×
---------------------------------------------------------
4943 cycles1,434,463×
84,365,083×
97,046,697×
22,639,105×
26,377,351×
738,683×
147,257,367×
13,851,132×
---48,746,880×
1,198,562,668×
-11,392,037×
--------------------------------------------------
5015 cycles754,516×
68,072,056×
17,480,311×
8,302,635×
-45,657,212×
12,571,741×
26,886,569×
------------1,737,072,262×
--------------------------------------------
5144 cycles1,323,595×
84,327,963×
83,072,720×
22,639,105×
26,377,351×
738,683×
147,257,367×
13,851,132×
-1,626,635,598×
-48,746,880×
151,108,959×
-11,392,037×
--------------------------------------------------
5217 cycles757,144×
68,139,684×
17,480,311×
1,251,213,764×
106,340,977×
45,657,212×
12,571,741×
26,886,569×
--------------------------1,029,573,434×
------------------------------
5350 cycles1,313,671×
84,327,963×
81,933,656×
136,110,975×
2,151,459,266×
738,683×
147,257,367×
130,438,299×
---48,746,880×
151,108,959×
-11,392,037×
--------------------------------------------------
5419 cycles1,162,752×
68,072,056×
17,480,311×
60,972,856×
13,242,826×
45,657,212×
1,834,815,850×
26,886,569×
----1,312,808,104×
----------------------------------------------------
5554 cycles1,312,475×
156,408,588×
84,468,557×
91,246,628×
227,194,065×
738,683×
147,257,367×
84,669,038×
---48,746,880×
151,108,959×
-11,392,037×
-------------------------------------------------2,868,351,411×
5622 cycles776,796×
68,072,056×
17,480,311×
60,972,856×
1,334,160,212×
45,657,212×
914,489,981×
1,522,396,262×
-462,159,673×
-------------------------------------------------------
5757 cycles1,314,235×
346,218,314×
82,658,804×
83,186,622×
227,194,065×
105,229,096×
147,257,367×
84,669,038×
---48,746,880×
151,108,959×
-11,392,037×
-----1,430,756,397×
------2,327,649,737×
-------------------------------------
5822 cycles756,124×
68,072,056×
17,480,311×
60,972,856×
33,369,626×
673,690,871×
209,592,935×
164,861,284×
116,013,844×
------------------------------4,398,762,204×
-------------------------
5963 cycles1,545,539×
127,413,814×
82,658,804×
83,186,622×
227,194,065×
44,043,839×
277,141,666×
84,669,038×
4,904,857,596×
--48,746,880×
151,108,959×
-11,392,037×
-----478,402,692×
--------------------------------------------
6021 cycles756,288×
68,072,056×
17,480,311×
60,972,856×
544,858,060×
45,657,212×
209,592,935×
6,444,620,041×
---------------------------------------------------------
6164 cycles1,337,779×
127,201,770×
82,658,804×
83,186,622×
227,194,065×
30,939,344×
254,541,212×
84,669,038×
454,115,519×
--48,746,880×
151,108,959×
-11,392,037×
----6,325,958,942×
478,402,692×
--------------------------------------------
6223 cycles8,296,568,869×
68,169,836×
17,480,311×
60,972,856×
142,185,553×
45,657,212×
209,592,935×
599,723,339×
---------------------------------------------------------
6368 cycles1,792,811×
127,201,770×
116,120,722×
8,560,691,882×
227,194,065×
30,939,344×
254,541,212×
176,877,738×
454,115,519×
--48,746,880×
151,108,959×
-11,392,037×
-----478,402,692×
--------------------------------------------
6429 cycles198,741,878×
68,072,056×
17,480,311×
60,972,856×
3,391,879,376×
632,705,855×
309,775,520×
599,723,339×
-------------------------------------6,689,665,145×
-------------------
6595 cycles1,321,019×
167,434,899×
224,502,323×
3,214,394,598×
227,194,065×
2,243,478,892×
254,541,212×
320,681,396×
454,115,519×
--5,693,558,429×
151,108,959×
-11,392,037×
-----478,402,692×
--------------------------------------------
6626 cycles198,474,254×
68,072,056×
17,480,311×
60,972,856×
430,156,423×
45,657,212×
209,592,935×
599,723,339×
----------------13,441,345,266×
----------------------------------------
67127 cycles1,322,995×
164,884,479×
141,142,202×
3,322,478,070×
227,194,065×
11,345,525,805×
254,541,212×
169,118,150×
454,115,519×
-101,080,651×
48,746,880×
151,108,959×
-11,392,037×
-----478,402,692×
--------------------------------------------
6834 cycles198,490,842×
68,072,056×
17,480,311×
60,972,856×
11,939,004,446×
45,657,212×
209,592,935×
599,723,339×
------------5,716,889,569×
--------------------------------------------
69130 cycles1,672,779×
150,305,012×
141,142,202×
3,247,696,946×
227,194,065×
4,203,923,207×
254,541,212×
180,490,111×
4,683,145,004×
--48,746,880×
151,108,959×
-11,392,037×
-----478,402,692×
-7,262,311,860×
------------------------------------------
7034 cycles198,464,946×
68,072,056×
17,480,311×
12,917,724,685×
1,336,773,122×
45,657,212×
209,592,935×
8,653,116,039×
---------------------------------------------------------
71136 cycles1,355,939×
256,658,239×
388,983,475×
3,247,696,946×
227,194,065×
4,254,744,935×
254,541,212×
174,438,828×
1,322,143,907×
--48,746,880×
151,108,959×
-11,392,037×
-----478,402,692×
-3,077,298,320×
-------------12,194,076,992×
----------------------------
7236 cycles199,075,234×
68,201,244×
17,480,311×
2,385,786,898×
1,336,773,122×
45,657,212×
209,592,935×
599,723,339×
----------------------------24,125,246,846×
----------------------------
73140 cycles1,352,759×
744,848,198×
235,215,400×
3,247,696,946×
227,194,065×
4,224,786,284×
254,541,212×
174,438,828×
1,322,143,907×
--48,746,880×
151,108,959×
-11,392,037×
--4,846,351,950×
10,024,342,851×
-478,402,692×
-1,790,933,754×
--------4,380,756,819×
---------------------------------
7439 cycles198,917,002×
68,072,056×
17,480,311×
1,382,645,989×
1,336,773,122×
45,657,212×
19,086,579,411×
13,399,775,271×
-105,569,767×
-------------------------------------------------------
75142 cycles1,329,323×
359,035,489×
235,215,400×
3,247,696,946×
227,194,065×
4,224,786,284×
254,541,212×
174,438,828×
22,314,192,983×
490,072,885×
-48,746,880×
151,108,959×
-11,392,037×
--3,032,901,505×
2,401,237,715×
-478,402,692×
-1,790,933,754×
------------------------------------------
7637 cycles198,509,178×
68,072,056×
17,480,311×
4,346,661,613×
1,364,077,121×
45,657,212×
209,592,935×
599,723,339×
------36,745,371,820×
--------------------------------------------------
77151 cycles41,691,001×
770,019,867×
235,215,400×
5,763,386,868×
265,371,866×
4,224,786,284×
1,064,896,873×
174,438,828×
2,093,060,461×
--48,746,880×
151,108,959×
-11,392,037×
--3,032,901,505×
2,401,237,715×
-478,402,692×
-1,790,933,754×
1,198,482,763×
--------9,632,617,836×
--14,745,819,772×
-----------------------------
7838 cycles198,501,970×
68,072,056×
17,480,311×
1,918,708,749×
1,336,773,122×
45,657,212×
47,451,868,178×
599,723,339×
------1,423,573,744×
--------------------------------------------------