Base 3: Cycles Lengths: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
012

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
10 cycles-----------------------------------------
20 cycles-----------------------------------------
31 cycle -
---------------------------------------
41 cycle -12×
---------------------------------------
51 cycle 18×
----------------------------------------
61 cycle --25×
--------------------------------------
72 cycles
26×
---------------------------------------
81 cycle 42×
----------------------------------------
93 cycles
11×
34×
--------------------------------------
102 cycles23×
--40×
-------------------------------------
115 cycles15×
11×
49×
--------------------------------------
122 cycles23×
65×
---------------------------------------
136 cycles11×
11×
30×
-50×
------------------------------------
143 cycles79×
38×
---------------------------------------
157 cycles11×
11×
30×
-23×
58×
-----------------------------------
164 cycles44×
38×
68×
--------------------------------------
1710 cycles19×
27×
30×
42×
23×
27×
-----------------------------------
185 cycles44×
38×
33×
-72×
------------------------------------
1912 cycles15×
19×
30×
93×
23×
27×
-----------------------------------
206 cycles60×
38×
130×
--------------------------------------
2113 cycles15×
19×
30×
54×
23×
27×
--82×
--------------------------------
227 cycles52×
126×
95×
--------------------------------------
2316 cycles23×
19×
54×
54×
23×
85×
--39×
--------------------------------
248 cycles52×
75×
95×
-100×
------------------------------------
2517 cycles19×
19×
42×
54×
23×
54×
--39×
-98×
------------------------------
269 cycles156×
75×
95×
-49×
------------------------------------
2719 cycles19×
35×
42×
54×
23×
54×
--39×
90×
47×
------------------------------
2810 cycles89×
75×
95×
-49×
124×
-----------------------------------
2922 cycles27×
27×
66×
54×
23×
54×
--121×
43×
47×
------------------------------
3011 cycles89×
75×
215×
-49×
65×
-----------------------------------
3123 cycles23×
27×
54×
54×
23×
54×
--78×
43×
47×
--122×
---------------------------
3214 cycles105×
107×
148×
84×
49×
65×
-----------------------------------
3326 cycles23×
27×
54×
54×
153×
54×
--78×
43×
47×
--59×
---------------------------
3415 cycles97×
91×
148×
41×
49×
201×
-----------------------------------
3530 cycles31×
27×
54×
54×
216×
54×
--78×
43×
47×
--59×
---------------------------
3616 cycles97×
91×
148×
250×
49×
65×
-----------------------------------
3733 cycles27×
43×
78×
54×
149×
54×
--78×
43×
47×
106×
-59×
---------------------------
3818 cycles129×
91×
268×
175×
49×
65×
-----------------------------------
3934 cycles27×
35×
66×
54×
149×
54×
--78×
43×
47×
51×
-59×
---154×
-----------------------
4019 cycles113×
91×
201×
175×
49×
65×
--164×
--------------------------------
4137 cycles35×
35×
66×
54×
149×
102×
--78×
43×
47×
157×
-59×
---75×
-----------------------
4220 cycles113×
259×
201×
175×
49×
65×
--81×
--------------------------------
4339 cycles31×
35×
66×
54×
149×
78×
--78×
213×
47×
102×
-59×
---75×
-----------------------
4423 cycles129×
160×
249×
175×
49×
189×
--81×
--------------------------------
4542 cycles31×
35×
66×
54×
149×
78×
178×
-78×
126×
47×
102×
-59×
---75×
-----------------------
4624 cycles121×
160×
225×
175×
233×
130×
--81×
--------------------------------
4747 cycles39×
51×
90×
86×
149×
78×
87×
-78×
126×
47×
208×
-59×
---75×
-----------------------
4825 cycles121×
160×
225×
175×
134×
130×
--81×
-196×
------------------------------
4948 cycles35×
43×
78×
70×
149×
78×
87×
-78×
126×
47×
153×
-59×
---75×
----194×
------------------
5026 cycles321×
160×
225×
175×
134×
130×
--81×
-97×
------------------------------
5150 cycles35×
43×
102×
70×
149×
78×
87×
-78×
126×
47×
153×
-59×
---75×
--178×
-95×
------------------
5228 cycles190×
192×
225×
175×
134×
130×
--81×
204×
97×
------------------------------
5355 cycles43×
43×
90×
134×
149×
78×
87×
138×
78×
126×
47×
153×
-59×
---75×
--87×
-95×
------------------
5429 cycles190×
176×
225×
175×
134×
346×
--81×
113×
97×
------------------------------
5556 cycles39×
43×
90×
102×
149×
78×
87×
67×
78×
126×
47×
153×
-59×
---75×
--87×
-95×
--218×
---------------
5632 cycles206×
176×
273×
175×
134×
231×
--245×
113×
97×
------------------------------
5759 cycles39×
59×
90×
102×
189×
78×
87×
67×
78×
126×
47×
153×
-59×
---75×
-170×
87×
-95×
--107×
---------------
5833 cycles198×
176×
481×
175×
134×
231×
--162×
113×
97×
------------------------------
5963 cycles47×
51×
90×
102×
169×
78×
87×
67×
304×
126×
47×
153×
-59×
---75×
-83×
87×
-95×
--107×
---------------
6034 cycles198×
176×
350×
175×
134×
231×
--162×
113×
97×
--252×
---------------------------
6164 cycles43×
51×
90×
102×
169×
78×
87×
67×
189×
126×
47×
153×
-59×
---75×
-83×
87×
-95×
--107×
--242×
------------
6237 cycles230×
240×
350×
327×
134×
231×
--162×
113×
97×
--129×
---------------------------
6365 cycles43×
51×
90×
102×
169×
78×
87×
67×
189×
126×
47×
153×
-59×
---75×
-83×
87×
-95×
--107×
--119×
250×
-----------
6440 cycles214×
208×
350×
244×
394×
231×
--162×
113×
97×
--129×
---------------------------
6572 cycles51×
51×
138×
102×
169×
280×
87×
67×
189×
126×
47×
153×
-59×
---75×
-83×
87×
-95×
--107×
--119×
123×
-----------
6641 cycles214×
208×
350×
244×
263×
231×
264×
-162×
113×
97×
--129×
---------------------------
6778 cycles47×
67×
114×
102×
169×
427×
87×
67×
189×
126×
47×
153×
-59×
---75×
-83×
87×
-95×
--107×
--119×
123×
-----------
6844 cycles230×
208×
350×
244×
648×
231×
--162×
113×
97×
--129×
---------------------------
6979 cycles47×
59×
114×
102×
169×
300×
87×
67×
189×
126×
47×
153×
-59×
---75×
-83×
87×
-95×
--107×
--119×
123×
--274×
--------
7046 cycles222×
208×
350×
524×
517×
231×
--162×
113×
97×
--129×
---------------------------
7182 cycles55×
59×
114×
102×
169×
300×
87×
67×
189×
126×
135×
153×
-59×
---75×
-83×
87×
186×
95×
--107×
--119×
123×
--135×
--------
7249 cycles222×
240×
398×
377×
517×
231×
--162×
113×
97×
212×
-129×
---------------------------
7383 cycles51×
59×
114×
102×
169×
300×
87×
67×
189×
126×
91×
153×
-59×
---75×
-83×
87×
91×
95×
--107×
--119×
123×
--135×
-290×
------
7451 cycles286×
224×
606×
377×
517×
231×
--162×
113×
97×
105×
-129×
---------------------------
7587 cycles51×
59×
114×
102×
169×
300×
87×
67×
487×
126×
91×
153×
-59×
---75×
-83×
87×
91×
95×
--107×
--119×
123×
--135×
-143×
------
7652 cycles254×
224×
475×
377×
517×
231×
--162×
113×
97×
105×
-129×
---316×
-----------------------
7792 cycles59×
75×
114×
134×
169×
300×
87×
67×
336×
206×
91×
153×
-59×
---75×
-253×
87×
91×
95×
--107×
--119×
123×
--135×
-143×
------
7853 cycles254×
224×
475×
377×
517×
231×
--474×
113×
97×
105×
-129×
---161×
-----------------------
7995 cycles55×
67×
138×
118×
209×
300×
87×
67×
336×
166×
91×
153×
-59×
---75×
-166×
87×
91×
95×
--107×
--119×
373×
--135×
-143×
------
8056 cycles270×
224×
475×
377×
517×
327×
--311×
113×
97×
317×
-129×
---161×
-----------------------
8196 cycles55×
67×
126×
118×
189×
300×
87×
67×
336×
166×
91×
153×
-59×
---75×
-166×
87×
91×
95×
--107×
--119×
246×
--135×
-143×
---322×
--
8257 cycles262×
552×
475×
377×
517×
279×
--311×
113×
97×
210×
-129×
---161×
-----------------------
83100 cycles63×
67×
150×
118×
189×
300×
87×
67×
408×
166×
91×
153×
-59×
---75×
-166×
87×
91×
95×
--107×
226×
-119×
246×
--135×
-143×
---159×
--
8459 cycles262×
357×
475×
377×
517×
279×
--311×
477×
97×
210×
-129×
---161×
-----------------------
85101 cycles59×
67×
138×
118×
189×
300×
87×
67×
372×
166×
91×
153×
-59×
---75×
-166×
87×
91×
95×
--107×
111×
-119×
246×
--135×
-143×
---159×
-338×
8662 cycles294×
357×
571×
377×
517×
495×
--311×
306×
97×
210×
-129×
---161×
-----------------------
87108 cycles59×
83×
138×
182×
189×
300×
87×
333×
372×
166×
91×
153×
-59×
---75×
-166×
87×
91×
95×
--107×
111×
-119×
246×
--135×
-143×
---159×
-167×
8865 cycles278×
357×
523×
377×
517×
380×
356×
-311×
306×
97×
210×
-129×
---161×
-----------------------
89111 cycles67×
75×
138×
150×
189×
300×
87×
198×
372×
166×
91×
153×
-171×
---75×
-166×
87×
91×
95×
--107×
111×
234×
119×
246×
--135×
-143×
---159×
-167×
9066 cycles278×
357×
523×
377×
877×
380×
177×
-311×
306×
97×
210×
-129×
---161×
-----------------------
91115 cycles63×
75×
138×
150×
189×
300×
87×
198×
372×
166×
453×
153×
-115×
---75×
-166×
87×
91×
95×
--107×
111×
115×
119×
246×
--135×
-143×
---159×
-167×
9271 cycles294×
389×
571×
441×
682×
380×
177×
-311×
306×
97×
430×
-129×
---161×
-----------------------
93120 cycles63×
75×
162×
150×
189×
348×
87×
198×
372×
166×
270×
451×
-115×
---75×
-166×
87×
91×
95×
--107×
111×
115×
119×
246×
--135×
-143×
---159×
-167×
9472 cycles286×
373×
547×
409×
682×
380×
177×
-311×
306×
473×
323×
-129×
---161×
-----------------------
95127 cycles71×
75×
150×
150×
309×
324×
87×
198×
372×
416×
270×
300×
-115×
---75×
-166×
87×
91×
95×
--107×
111×
115×
119×
246×
--135×
-143×
---159×
-167×
9673 cycles286×
373×
547×
409×
682×
380×
177×
-311×
306×
278×
323×
-129×
---161×
----388×
------------------
97130 cycles67×
91×
150×
150×
249×
324×
87×
198×
444×
289×
270×
300×
-115×
---75×
-166×
87×
91×
95×
--107×
111×
115×
119×
246×
--135×
-143×
298×
--159×
-167×
9874 cycles678×
373×
547×
409×
682×
380×
177×
-311×
306×
278×
323×
-129×
---161×
----193×
------------------
99132 cycles67×
83×
150×
150×
249×
324×
87×
198×
408×
289×
270×
300×
-115×
---75×
-166×
87×
91×
95×
394×
-107×
111×
115×
119×
246×
--135×
-143×
147×
--159×
-167×
10076 cycles419×
373×
595×
409×
682×
380×
177×
-311×
306×
278×
323×
-129×
---161×
--412×
-193×
------------------