Base 38: Iteration Frequencies: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl

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 1 2 3 4 5 6 7 8 9 10
Average Steps
Cycle Start		0.97 step
avg		1.45 step
avg		8.73 step
avg		3.14 step
avg		9.07 step
avg		19.33 step
avg		14.06 step
avg		43.37 step
avg		13.94 step
avg		92.86 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
37×
0s:
1s:
2s:
11×
388×
342×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
1×
417×
378×
754×
746×
734×
718×
698×
674×
646×
614×
578×
538×
494×
446×
394×
338×
278×
214×
146×
74×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
5,797×
14,328×
57,456×
11,112×
9,609×
1,791×
1,176×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
1×
10,549×
14,582×
15,932×
36,872×
54,124×
78,668×
87,424×
94,720×
77,268×
92,440×
83,174×
59,824×
49,140×
31,070×
23,984×
18,772×
13,380×
7,990×
754×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
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15s:
16s:
17s:
18s:
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21s:
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25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
1×
64,395×
154,805×
154,625×
140,503×
166,791×
186,078×
186,668×
207,208×
202,532×
201,234×
178,348×
177,260×
208,974×
273,151×
300,303×
251,759×
227,052×
218,653×
204,561×
189,342×
167,832×
140,798×
145,151×
153,014×
118,940×
141,766×
88,379×
82,595×
74,860×
36,733×
31,433×
37,161×
53,932×
37,885×
44,250×
49,752×
41,780×
63,409×
56,561×
56,464×
65,091×
55,548×
44,300×
31,270×
39,093×
55,556×
35,173×
27,729×
24,055×
18,500×
21,524×
24,384×
25,794×
18,826×
15,355×
15,643×
16,620×
5,667×
10,058×
5,739×
15,152×
8,439×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
1×
42,547×
113,572×
223,046×
355,520×
354,768×
531,008×
864,788×
1,106,216×
1,539,328×
2,091,432×
2,485,286×
2,805,256×
3,295,654×
3,774,572×
3,721,404×
3,814,030×
3,553,292×
2,846,720×
1,879,962×
1,440,112×
858,050×
337,920×
203,508×
76,586×
4,710×
1,280×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
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71s:
72s:
73s:
74s:
75s:
76s:
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78s:
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81s:
82s:
83s:
84s:
85s:
86s:
87s:
88s:
89s:
90s:
91s:
92s:
93s:
94s:
95s:
96s:
97s:
98s:
99s:
100s:
101s:
102s:
103s:
104s:
105s:
106s:
107s:
108s:
109s:
110s:
111s:
112s:
113s:
114s:
115s:
116s:
117s:
118s:
119s:
120s:
121s:
122s:
123s:
124s:
125s:
126s:
127s:
128s:
129s:
130s:
131s:
132s:
133s:
134s:
135s:
136s:
137s:
138s:
139s:
140s:
141s:
142s:
143s:
144s:
145s:
146s:
147s:
148s:
149s:
150s:
1×
542,825×
2,263,724×
2,422,099×
3,125,906×
3,422,835×
3,085,632×
3,003,119×
2,955,429×
2,726,262×
3,070,829×
3,591,659×
3,854,336×
3,518,327×
3,239,615×
3,324,029×
3,796,304×
3,664,929×
3,530,398×
3,291,756×
3,497,762×
2,781,159×
2,692,827×
2,796,158×
3,108,028×
3,127,697×
3,144,109×
3,102,334×
2,679,975×
2,583,864×
2,508,129×
2,570,339×
2,415,826×
2,415,398×
1,988,976×
1,825,722×
1,969,316×
2,489,034×
2,265,501×
2,611,619×
2,765,635×
2,252,232×
2,461,519×
2,545,454×
2,879,576×
2,243,813×
2,478,751×
2,414,483×
2,287,598×
2,026,009×
1,980,832×
2,011,675×
2,192,370×
2,128,728×
1,903,950×
1,793,779×
1,800,330×
1,839,421×
1,611,297×
1,826,511×
1,827,382×
1,751,287×
1,632,749×
1,662,710×
1,569,495×
1,699,976×
1,579,506×
1,606,841×
1,477,135×
1,495,214×
1,468,686×
1,509,621×
1,491,820×
1,472,032×
1,653,361×
1,413,407×
1,324,961×
1,218,701×
1,154,260×
1,247,109×
1,199,815×
1,391,878×
1,310,236×
1,378,243×
1,426,682×
1,266,341×
1,072,075×
1,166,777×
1,040,304×
792,180×
918,429×
1,199,726×
984,100×
808,053×
808,811×
827,437×
1,100,327×
1,279,623×
988,339×
656,717×
502,857×
601,324×
559,080×
495,744×
453,779×
452,948×
278,033×
323,813×
394,281×
408,703×
160,342×
128,122×
100,701×
125,643×
110,052×
122,459×
107,656×
93,394×
111,334×
129,423×
200,452×
171,699×
138,137×
83,902×
46,160×
62,675×
113,543×
90,330×
145,478×
136,752×
206,690×
203,131×
214,534×
148,669×
108,369×
99,596×
54,097×
99,896×
77,827×
89,489×
101,648×
166,300×
156,904×
145,589×
123,301×
106,786×
81,288×
71,096×
41,297×
59,152×
28,624×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
1×
666,531×
3,421,794×
8,984,238×
19,455,284×
37,736,352×
58,101,078×
70,043,166×
78,418,968×
86,613,252×
88,113,896×
83,981,056×
62,033,986×
43,635,804×
32,431,826×
30,725,644×
32,460,808×
32,467,358×
38,472,946×
32,635,906×
42,242,490×
35,208,776×
26,938,444×
16,934,494×
18,385,694×
25,065,912×
26,332,682×
25,575,760×
12,048,590×
6,605,424×
2,980,798×
3,581,582×
4,276,316×
5,581,832×
4,477,272×
3,490,718×
1,028,904×
560,748×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
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31s:
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34s:
35s:
36s:
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41s:
42s:
43s:
44s:
45s:
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49s:
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51s:
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53s:
54s:
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56s:
57s:
58s:
59s:
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133s:
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137s:
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250s:
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253s:
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255s:
256s:
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261s:
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263s:
264s:
265s:
266s:
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268s:
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273s:
274s:
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281s:
282s:
283s:
284s:
285s:
286s:
287s:
288s:
289s:
290s:
291s:
292s:
293s:
294s:
295s:
296s:
297s:
1×
1,487,777×
12,759,892×
20,326,449×
23,562,723×
26,758,064×
28,474,603×
29,245,664×
26,045,663×
24,753,776×
26,595,774×
30,586,494×
29,666,531×
28,722,449×
29,893,434×
30,927,350×
31,797,029×
29,684,326×
32,674,871×
28,800,392×
28,413,155×
28,523,236×
28,522,553×
34,708,242×
38,314,757×
36,009,763×
36,122,428×
33,334,132×
33,439,339×
30,936,330×
29,359,375×
35,463,647×
35,495,641×
32,179,050×
36,614,534×
39,932,011×
37,451,413×
36,779,872×
34,115,392×
36,652,389×
40,514,357×
40,019,097×
39,777,561×
43,883,585×
40,633,117×
41,124,461×
41,149,430×
41,539,029×
38,692,043×
35,929,049×
41,205,792×
45,014,701×
49,734,406×
42,530,985×
41,152,331×
42,750,232×
43,283,209×
40,406,517×
33,846,848×
31,815,254×
37,169,572×
34,061,565×
32,254,620×
33,352,145×
36,108,073×
40,778,790×
36,471,080×
33,948,812×
35,075,666×
37,719,742×
39,369,686×
34,165,864×
30,515,990×
34,641,744×
34,289,542×
33,684,062×
27,367,032×
22,002,892×
21,185,826×
21,564,144×
22,739,335×
19,226,681×
17,105,655×
18,655,215×
23,402,696×
25,626,410×
28,518,516×
26,120,851×
24,868,243×
24,408,466×
23,188,068×
26,261,254×
24,239,681×
21,378,247×
16,652,866×
17,963,501×
21,131,611×
22,184,454×
20,789,964×
19,765,943×
19,675,438×
16,538,000×
16,043,947×
17,688,847×
19,388,157×
14,962,670×
13,429,312×
12,914,633×
10,985,103×
13,179,840×
18,203,872×
24,222,845×
23,769,704×
22,319,225×
21,799,380×
22,899,827×
29,913,427×
27,254,805×
22,692,517×
22,494,618×
24,273,477×
23,881,433×
27,726,137×
24,715,879×
22,694,838×
22,153,120×
21,956,551×
22,651,266×
25,913,342×
26,273,144×
26,641,060×
27,216,845×
24,326,626×
24,929,365×
25,336,599×
27,376,194×
26,609,269×
30,357,749×
27,914,789×
23,548,840×
21,459,154×
21,422,209×
20,780,177×
20,228,028×
21,596,669×
24,265,307×
24,158,008×
21,296,766×
17,935,253×
14,819,182×
14,108,903×
14,508,720×
15,361,572×
17,987,104×
16,419,878×
14,416,670×
12,625,447×
15,350,670×
16,581,010×
17,006,332×
16,358,971×
13,395,974×
12,594,796×
15,936,352×
15,458,574×
12,746,302×
13,628,928×
11,807,077×
11,193,673×
10,839,841×
10,645,528×
10,004,897×
11,202,321×
8,944,135×
11,390,851×
12,384,114×
13,470,658×
13,177,417×
12,088,893×
12,707,131×
9,833,952×
9,081,936×
8,485,644×
8,825,809×
9,737,152×
13,596,419×
12,831,823×
13,831,263×
15,281,173×
14,498,080×
12,094,360×
9,309,092×
10,773,828×
12,521,600×
15,138,824×
17,951,286×
15,277,899×
11,377,664×
9,251,384×
9,816,285×
6,199,067×
6,490,436×
6,565,618×
7,259,124×
7,234,664×
8,962,039×
9,510,320×
7,591,181×
6,509,160×
5,026,771×
3,790,846×
3,542,177×
3,271,297×
4,292,664×
3,888,398×
3,848,780×
3,716,311×
3,782,374×
2,687,273×
2,910,016×
2,742,042×
3,642,582×
4,258,864×
6,009,988×
4,995,022×
3,914,089×
2,671,166×
2,423,401×
2,153,199×
2,454,131×
3,830,921×
6,321,379×
5,182,570×
7,875,242×
9,538,346×
11,362,484×
7,815,091×
6,241,488×
5,611,499×
5,665,684×
6,204,125×
6,549,589×
6,612,327×
4,953,778×
4,317,442×
3,881,284×
3,465,262×
4,019,545×
3,460,111×
2,198,882×
2,546,598×
2,293,790×
2,423,314×
2,054,237×
1,694,195×
1,705,217×
2,615,661×
2,841,433×
3,295,949×
2,686,402×
2,064,387×
2,204,349×
2,118,099×
2,005,540×
1,563,695×
1,325,175×
3,581,569×
4,471,976×
2,568,108×
2,687,550×
1,875,329×
1,724,683×
1,497,649×
3,182,912×
3,026,852×
2,211,175×
1,752,427×
1,876,274×
1,840,298×
1,520,966×
1,917,785×
1,606,611×
557,765×
618,928×
500,229×
615,510×
478,775×
503,572×
673,387×
333,920×
632,570×
861,354×
2,059,536×
706,863×
410,787×
77,905×
4,708×
22,004×