Base 5: Cycles Lengths: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
01234

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-----------------------------------------
21 cycle 
----------------------------------------
31 cycle -30×
---------------------------------------
41 cycle 65×
----------------------------------------
51 cycle ---121×
-------------------------------------
61 cycle ----205×
------------------------------------
71 cycle ---325×
-------------------------------------
81 cycle -----490×
-----------------------------------
91 cycle 710×
----------------------------------------
101 cycle ---996×
-------------------------------------
112 cycles28×
-1,332×
--------------------------------------
121 cycle -------1,815×
---------------------------------
133 cycles28×
-124×
-2,223×
------------------------------------
142 cycles---624×
2,431×
------------------------------------
156 cycles28×
395×
124×
694×
253×
2,377×
-----------------------------------
163 cycles888×
--3,559×
393×
------------------------------------
179 cycles28×
821×
124×
4,162×
253×
592×
-----------------------------------
182 cycles216×
---7,094×
------------------------------------
1914 cycles28×
304×
1,019×
6,654×
253×
592×
-----------------------------------
202 cycles216×
-10,405×
--------------------------------------
2116 cycles28×
304×
649×
3,144×
253×
592×
--7,675×
--------------------------------
224 cycles216×
-1,664×
-13,065×
------------------------------------
2323 cycles520×
634×
1,716×
3,144×
253×
8,899×
--2,379×
--------------------------------
244 cycles216×
-1,664×
-13,672×
-----4,918×
------------------------------
2526 cycles206×
392×
906×
3,144×
253×
3,295×
--2,379×
-13,171×
------------------------------
264 cycles216×
-1,664×
-5,875×
----19,645×
-------------------------------
2730 cycles206×
392×
906×
3,144×
253×
3,295×
--2,379×
16,515×
4,370×
------------------------------
285 cycles216×
10,571×
1,664×
-5,875×
17,629×
-----------------------------------
2936 cycles206×
392×
2,324×
3,144×
253×
3,295×
--21,073×
5,858×
4,370×
------------------------------
307 cycles6,662×
916×
1,664×
-5,875×
3,650×
--27,604×
--------------------------------
3140 cycles206×
392×
1,461×
3,144×
253×
3,295×
--9,248×
5,858×
4,370×
--24,128×
---------------------------
3211 cycles2,272×
11,586×
1,664×
33,853×
5,875×
3,650×
-----------------------------------
3354 cycles206×
392×
1,461×
4,224×
28,244×
3,295×
--9,248×
5,858×
4,370×
--8,742×
---------------------------
3411 cycles2,272×
3,778×
1,664×
17,234×
5,875×
42,987×
-----------------------------------
3568 cycles206×
392×
1,461×
3,144×
45,530×
3,295×
--9,248×
5,858×
4,370×
--8,742×
---------------------------
3614 cycles2,272×
3,778×
1,664×
74,146×
5,875×
3,650×
-----------------------------------
3777 cycles775×
392×
1,461×
3,144×
24,677×
9,673×
--9,248×
5,858×
4,370×
32,925×
-8,742×
---------------------------
3816 cycles2,272×
3,778×
52,904×
29,118×
5,875×
17,978×
-----------------------------------
3983 cycles386×
392×
1,461×
3,144×
24,677×
9,599×
--9,248×
5,858×
4,370×
12,981×
-8,742×
---42,547×
-----------------------
4018 cycles2,272×
3,778×
32,636×
29,118×
5,875×
3,650×
--58,417×
--------------------------------
4195 cycles386×
1,282×
1,461×
4,368×
24,677×
18,470×
--9,248×
5,858×
4,370×
53,373×
-8,742×
---16,755×
-----------------------
4219 cycles2,272×
3,778×
28,386×
29,118×
5,875×
3,650×
--22,832×
--67,269×
-----------------------------
43107 cycles386×
781×
1,461×
3,656×
24,677×
10,466×
--9,248×
67,193×
4,370×
30,625×
-8,742×
---16,755×
-----------------------
4425 cycles7,726×
7,596×
44,910×
29,118×
5,875×
76,518×
--22,832×
--------------------------------
45126 cycles386×
781×
1,461×
3,656×
24,677×
10,466×
70,243×
-9,248×
30,461×
4,370×
30,625×
-8,742×
---16,755×
-----------------------
4627 cycles3,732×
5,118×
33,458×
29,118×
100,448×
35,589×
--22,832×
--------------------------------
47144 cycles386×
2,406×
3,415×
11,378×
24,677×
16,163×
28,884×
-9,248×
30,461×
4,370×
93,010×
-8,742×
---16,755×
-----------------------
4829 cycles3,732×
5,118×
33,458×
29,118×
23,918×
35,589×
--22,832×
-116,955×
------------------------------
49150 cycles386×
1,495×
2,233×
5,704×
24,677×
12,922×
28,884×
-9,248×
30,461×
4,370×
57,620×
-8,742×
---16,755×
----89,323×
------------------
5030 cycles3,732×
5,118×
33,458×
29,118×
23,918×
35,589×
115,203×
-22,832×
-47,278×
------------------------------
51160 cycles1,062×
1,495×
2,233×
5,704×
24,677×
12,922×
32,017×
-9,248×
30,461×
4,370×
57,620×
-8,742×
---16,755×
--96,826×
-36,918×
------------------
5233 cycles3,732×
5,118×
33,458×
29,118×
23,918×
35,589×
--22,832×
166,242×
47,278×
------------------------------
53188 cycles630×
1,495×
2,233×
24,887×
24,677×
12,922×
30,333×
93,053×
9,248×
30,461×
4,370×
57,620×
-8,742×
---16,755×
--40,661×
-36,918×
------------------
5435 cycles3,732×
45,387×
33,458×
29,118×
23,918×
179,516×
--22,832×
39,026×
47,278×
------------------------------
55196 cycles630×
1,495×
2,233×
13,856×
24,677×
12,922×
30,333×
39,564×
9,248×
30,461×
4,370×
57,620×
-8,742×
---16,755×
--40,661×
-36,918×
--124,636×
---------------
5641 cycles3,732×
14,805×
42,106×
29,118×
23,918×
72,833×
--214,814×
39,026×
47,278×
------------------------------
57209 cycles630×
1,495×
2,233×
13,856×
27,608×
12,922×
30,333×
39,564×
9,248×
43,230×
4,370×
57,620×
-8,742×
---16,755×
-123,027×
40,661×
-36,918×
--52,638×
---------------
5842 cycles168,739×
14,805×
37,050×
29,118×
23,918×
72,833×
--125,073×
39,026×
47,278×
------------------------------
59238 cycles630×
1,495×
6,726×
13,856×
25,945×
12,922×
30,333×
39,564×
157,790×
36,060×
4,370×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
-36,918×
--52,638×
---------------
6046 cycles22,952×
14,805×
37,050×
29,118×
23,918×
72,833×
--125,073×
39,026×
47,278×
--223,318×
---------------------------
61247 cycles630×
1,495×
4,210×
13,856×
25,945×
12,922×
30,333×
39,564×
73,418×
36,060×
4,370×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
-36,918×
--52,638×
--168,263×
------------
6250 cycles22,952×
96,912×
37,050×
163,036×
23,918×
72,833×
--125,073×
39,026×
47,278×
--92,637×
---------------------------
63257 cycles630×
1,495×
4,210×
13,856×
25,945×
12,922×
30,333×
39,564×
73,418×
41,326×
4,370×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
-36,918×
--52,638×
--72,416×
180,021×
-----------
6463 cycles22,952×
47,076×
37,050×
74,476×
255,979×
72,833×
--125,073×
39,026×
47,278×
--92,637×
---------------------------
65313 cycles1,490×
2,158×
24,280×
13,856×
25,945×
194,016×
30,333×
39,564×
73,418×
38,649×
4,370×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
-36,918×
--52,638×
--72,416×
78,032×
-----------
6664 cycles22,952×
47,076×
37,050×
74,476×
119,950×
72,833×
238,539×
-125,073×
39,026×
47,278×
--92,637×
---------------------------
67367 cycles938×
3,217×
11,768×
13,856×
25,945×
313,155×
30,333×
39,564×
73,418×
38,649×
4,370×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
-36,918×
--52,638×
--72,416×
78,032×
-----------
6878 cycles22,952×
47,076×
37,050×
74,476×
470,384×
72,833×
--125,073×
39,026×
47,278×
--92,637×
---------------------------
69378 cycles938×
2,412×
11,768×
13,856×
25,945×
189,475×
30,333×
39,564×
73,418×
38,649×
12,939×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
-36,918×
--52,638×
--72,416×
78,032×
--232,711×
--------
7082 cycles22,952×
47,076×
37,050×
448,238×
218,458×
72,833×
--125,073×
39,026×
47,278×
--92,637×
---------------------------
71397 cycles938×
2,412×
11,768×
13,856×
25,945×
189,475×
30,333×
39,564×
73,418×
38,649×
45,749×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
223,658×
36,918×
--52,638×
--72,416×
78,032×
--103,263×
--------
7291 cycles27,340×
47,076×
37,050×
235,356×
218,458×
107,398×
--125,073×
39,026×
47,278×
306,278×
-92,637×
---------------------------
73408 cycles938×
2,412×
11,768×
13,856×
25,945×
189,475×
30,333×
39,564×
73,418×
38,649×
24,134×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
99,351×
36,918×
--52,638×
--72,416×
78,032×
--103,263×
-283,747×
------
7492 cycles24,040×
47,076×
364,393×
235,356×
218,458×
87,965×
--125,073×
39,026×
47,278×
145,118×
-92,637×
---------------------------
75456 cycles938×
2,412×
23,443×
13,856×
25,945×
189,475×
30,333×
39,564×
369,378×
38,649×
24,134×
57,620×
-8,742×
---16,755×
-52,635×
40,661×
99,351×
36,918×
--52,638×
--72,416×
78,032×
--103,263×
-125,338×
------
7698 cycles24,040×
47,076×
118,939×
235,356×
218,458×
131,917×
--125,073×
39,026×
47,278×
145,118×
-92,637×
---356,657×
-----------------------
77484 cycles938×
4,774×
17,053×
21,087×
25,945×
189,475×
30,333×
39,564×
205,148×
85,997×
24,134×
57,620×
-8,742×
---16,755×
-327,553×
40,661×
99,351×
36,918×
--52,638×
--72,416×
78,032×
--103,263×
-125,338×
------
78101 cycles24,040×
47,076×
158,845×
235,356×
218,458×
96,233×
--495,404×
39,026×
47,278×
145,118×
-92,637×
---149,584×
-----------------------
79502 cycles1,934×
3,500×
17,053×
17,016×
29,797×
189,475×
30,333×
39,564×
205,148×
58,501×
24,134×
57,620×
-8,742×
22,357×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
--72,416×
408,078×
--103,263×
-125,338×
------
80113 cycles24,040×
53,068×
135,779×
254,390×
218,458×
162,227×
--245,238×
39,026×
47,278×
507,771×
-92,637×
---149,584×
-----------------------
81515 cycles1,310×
3,500×
17,053×
17,016×
27,693×
189,475×
30,333×
39,564×
205,148×
58,501×
24,134×
57,620×
14,319×
8,742×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
--72,416×
224,578×
--103,263×
-125,338×
---370,768×
--
82114 cycles24,040×
49,548×
135,779×
240,694×
218,458×
121,451×
451,443×
-245,238×
39,026×
47,278×
308,374×
-92,637×
---149,584×
-----------------------
83538 cycles1,310×
3,500×
20,225×
17,016×
27,693×
189,475×
30,333×
39,564×
244,369×
58,501×
24,134×
57,620×
4,329×
8,742×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
370,794×
-72,416×
224,578×
--103,263×
-125,338×
---168,681×
--
84125 cycles24,040×
49,548×
135,779×
240,694×
218,458×
121,451×
--245,238×
698,804×
47,278×
308,374×
-92,637×
---149,584×
-----------------------
85551 cycles1,310×
3,500×
18,401×
17,016×
27,693×
189,475×
30,333×
39,564×
221,124×
58,501×
24,134×
57,620×
4,329×
8,742×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
-72,416×
224,578×
--103,263×
-125,338×
---168,681×
-442,523×
86132 cycles40,430×
74,178×
311,611×
240,694×
218,458×
490,054×
--245,238×
336,649×
47,278×
308,374×
-92,637×
---149,584×
-----------------------
87627 cycles1,310×
3,500×
18,401×
57,594×
27,693×
189,475×
30,333×
473,413×
221,124×
58,501×
24,134×
57,620×
4,329×
8,742×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
-72,416×
224,578×
--103,263×
-125,338×
---168,681×
-199,140×
88151 cycles30,216×
60,448×
221,771×
240,694×
218,458×
291,572×
551,231×
-245,238×
336,649×
47,278×
308,374×
-92,637×
---149,584×
-----------------------
89651 cycles1,310×
3,500×
18,401×
35,790×
27,693×
189,475×
30,333×
235,475×
221,124×
58,501×
24,134×
57,620×
4,329×
85,019×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
430,530×
72,416×
224,578×
--103,263×
-125,338×
---168,681×
-199,140×
90152 cycles30,216×
60,448×
221,771×
240,694×
792,217×
291,572×
232,818×
-245,238×
336,649×
47,278×
308,374×
-92,637×
---149,584×
-----------------------
91707 cycles1,310×
3,500×
18,401×
35,790×
27,693×
189,475×
30,333×
235,475×
221,124×
58,501×
564,557×
57,620×
4,329×
41,308×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
197,628×
72,416×
224,578×
--103,263×
-125,338×
---168,681×
-199,140×
92169 cycles30,216×
77,452×
231,335×
281,642×
363,267×
366,892×
232,818×
-245,238×
336,649×
47,278×
866,947×
-92,637×
---149,584×
-----------------------
93768 cycles2,490×
5,308×
18,401×
46,481×
27,693×
228,971×
30,333×
235,475×
221,124×
58,501×
269,089×
581,208×
4,329×
41,308×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
197,628×
72,416×
224,578×
--103,263×
-125,338×
---168,681×
-199,140×
94172 cycles30,216×
67,264×
226,131×
255,596×
363,267×
335,112×
232,818×
-245,238×
336,649×
733,807×
543,956×
-92,637×
---149,584×
-----------------------
95845 cycles1,746×
4,316×
18,401×
41,359×
115,180×
206,765×
30,333×
235,475×
221,124×
584,501×
269,089×
296,321×
4,329×
41,308×
10,663×
--16,755×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
197,628×
72,416×
224,578×
--103,263×
-125,338×
---168,681×
-199,140×
96180 cycles30,216×
67,264×
226,131×
257,874×
363,267×
335,112×
232,818×
-245,238×
336,649×
325,381×
543,956×
-92,637×
---149,584×
----715,093×
------------------
97868 cycles1,746×
4,316×
20,706×
41,359×
65,688×
206,765×
30,333×
235,475×
238,182×
300,803×
269,089×
296,321×
4,329×
41,308×
10,663×
--51,699×
-177,023×
40,661×
99,351×
36,918×
--52,638×
169,071×
197,628×
72,416×
224,578×
--103,263×
-125,338×
597,432×
--168,681×
-199,140×
98180 cycles30,216×
67,264×
226,131×
255,596×
363,267×
335,112×
232,818×
-245,238×
336,649×
325,381×
543,956×
-824,600×
---149,584×
----313,758×
------------------
99900 cycles1,746×
4,316×
19,629×
41,359×
65,688×
206,765×
30,333×
251,139×
228,580×
300,803×
269,089×
296,321×
4,329×
41,308×
10,663×
--31,381×
-177,023×
40,661×
99,351×
36,918×
677,147×
-52,638×
169,071×
197,628×
72,416×
224,578×
--103,263×
-125,338×
273,968×
--168,681×
-199,140×
100189 cycles33,116×
67,264×
226,131×
255,596×
363,267×
335,112×
258,910×
-245,238×
336,649×
325,381×
543,956×
-92,637×
---149,584×
--1,051,522×
-313,758×
------------------