Base 39: Iteration Frequencies: Full Cycle

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
Full Cycle		1.97 step
avg		5.57 step
avg		10.41 step
avg		12.88 step
avg		12.39 step
avg		49.59 step
avg		21.42 step
avg		68.05 step
avg		35.12 step
avg		77.14 step
avg
Step Frequency
Full Cycle
0s:
1s:
2s:
0×
1×
38×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
0×
1×
39×
64×
68×
152×
152×
304×
0s:
1s:
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3s:
4s:
5s:
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21s:
22s:
0×
1×
38×
799×
396×
790×
780×
766×
748×
726×
700×
670×
636×
598×
556×
510×
460×
406×
348×
286×
220×
150×
76×
0s:
1s:
2s:
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5s:
6s:
7s:
8s:
9s:
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11s:
12s:
13s:
14s:
15s:
16s:
0×
1×
38×
0×
546×
1,251×
0×
4,166×
10,290×
921×
0×
0×
0×
21,508×
65,010×
7,800×
399×
0s:
1s:
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18s:
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21s:
22s:
0×
1×
2,586×
4,411×
6,802×
15,162×
24,388×
43,016×
63,629×
74,743×
68,589×
97,822×
95,001×
86,467×
88,032×
79,989×
62,293×
54,987×
43,678×
29,381×
15,136×
5,290×
1,195×
0s:
1s:
2s:
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73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
81s:
82s:
83s:
84s:
0×
1×
38×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
17,898×
47,546×
96,224×
189,854×
278,397×
185,544×
152,393×
168,510×
96,516×
81,876×
83,558×
73,894×
77,875×
68,829×
74,069×
168,708×
170,683×
221,063×
273,373×
181,396×
169,628×
187,340×
160,505×
217,616×
344,325×
243,028×
158,218×
173,571×
100,792×
77,086×
85,559×
154,121×
147,124×
134,863×
105,195×
162,086×
124,710×
114,198×
169,433×
141,642×
102,316×
74,120×
103,278×
78,809×
100,632×
86,439×
87,031×
67,981×
74,844×
76,191×
71,375×
71,831×
77,844×
59,841×
19,007×
16,271×
6,325×
1,467×
1,482×
2,683×
0s:
1s:
2s:
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33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
0×
1×
38×
0×
0×
0×
0×
0×
0×
92,372×
240,755×
445,480×
829,572×
1,225,844×
1,720,384×
2,135,241×
2,584,665×
3,002,050×
3,499,128×
3,713,175×
3,979,069×
4,449,483×
3,358,239×
2,683,515×
1,692,764×
1,184,905×
755,123×
540,825×
407,126×
363,301×
539,514×
636,809×
763,417×
965,108×
1,009,430×
755,274×
453,982×
416,320×
440,054×
292,934×
150,010×
45,998×
4,100×
3,615×
0s:
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153s:
154s:
155s:
0×
1×
4,770×
14,038×
0×
29,611×
94,643×
349,102×
212,726×
134,394×
132,526×
371,016×
539,207×
1,136,335×
1,039,016×
1,137,752×
1,433,821×
1,138,560×
1,538,809×
3,666,022×
3,549,960×
3,497,078×
2,841,512×
2,849,474×
3,319,649×
4,203,580×
4,106,687×
2,818,223×
1,920,194×
1,668,425×
1,284,787×
1,551,120×
1,180,551×
1,414,515×
1,057,260×
780,597×
1,574,599×
1,347,527×
1,519,395×
1,535,258×
2,246,625×
1,922,423×
1,599,475×
1,430,061×
1,298,692×
1,540,927×
1,186,457×
1,106,067×
1,292,794×
1,697,814×
1,386,632×
1,283,685×
1,184,099×
1,236,749×
1,907,378×
1,753,665×
1,834,465×
1,563,738×
2,426,365×
2,735,535×
3,550,867×
4,043,969×
4,731,229×
4,717,483×
4,405,531×
4,650,722×
3,714,967×
4,627,981×
4,459,559×
3,450,975×
3,572,896×
4,468,615×
4,085,370×
3,643,222×
2,812,198×
3,466,220×
3,653,806×
3,319,158×
3,104,156×
3,102,530×
2,713,679×
2,535,553×
2,629,576×
2,956,170×
2,418,546×
1,946,489×
2,176,231×
2,856,685×
2,816,843×
3,119,738×
3,421,988×
3,371,289×
2,861,204×
2,986,681×
2,552,414×
2,898,293×
2,943,767×
2,791,562×
1,748,870×
1,912,957×
1,589,255×
2,062,329×
2,000,143×
1,816,166×
1,178,890×
1,106,608×
936,065×
869,594×
761,392×
776,019×
1,802,290×
2,064,097×
2,518,492×
1,914,792×
1,611,971×
1,896,918×
1,708,183×
1,452,174×
1,100,049×
971,004×
1,133,402×
866,102×
528,326×
477,198×
840,736×
597,052×
509,203×
735,213×
597,831×
263,515×
159,892×
305,542×
383,936×
200,494×
263,127×
138,593×
154,997×
196,589×
209,525×
242,038×
53,366×
7,513×
43,765×
251,836×
270,686×
172,774×
130,757×
64,336×
55,164×
43,160×
2,809×
19,198×
1,148×
6,636×
2,890×
660×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
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47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
0×
1×
89,702×
511,847×
1,426,053×
1,938,406×
4,725,193×
6,404,610×
8,844,283×
9,735,804×
9,055,981×
10,371,702×
9,909,737×
10,416,619×
9,858,495×
10,551,468×
7,290,244×
5,923,952×
4,099,320×
3,549,111×
1,377,210×
741,652×
448,376×
44,224×
1,008,979×
4,794,509×
11,604,620×
22,403,236×
42,088,074×
55,707,890×
75,606,867×
75,370,608×
70,629,649×
69,775,790×
62,375,744×
57,491,371×
51,652,173×
49,009,771×
51,885,482×
47,661,851×
60,457,345×
59,259,070×
68,248,820×
65,839,267×
59,602,078×
47,838,943×
38,736,936×
32,402,333×
21,433,833×
16,799,712×
11,966,595×
5,706,400×
2,236,676×
2,135,582×
2,254,968×
1,063,126×
246,249×
32,868×
7,740×
0s:
1s:
2s:
3s:
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169s:
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171s:
172s:
173s:
174s:
175s:
176s:
0×
1×
16,410×
51,700×
564,053×
1,392,902×
3,126,034×
3,465,531×
3,995,663×
3,833,641×
2,468,784×
3,873,116×
3,887,445×
3,359,591×
2,738,390×
3,865,557×
7,151,853×
5,479,721×
9,862,059×
19,670,411×
17,818,146×
14,712,578×
18,656,524×
19,188,063×
27,075,782×
35,311,149×
31,744,947×
19,052,810×
19,409,220×
18,100,640×
20,742,737×
32,243,019×
39,776,984×
37,805,571×
26,178,656×
27,429,603×
27,585,767×
23,495,135×
22,109,025×
27,015,986×
29,479,689×
29,576,609×
37,791,498×
46,945,952×
65,878,228×
72,067,585×
64,021,559×
48,091,066×
47,815,891×
45,138,899×
52,113,694×
82,281,091×
81,926,798×
86,291,097×
73,482,272×
81,682,255×
83,492,347×
78,715,830×
85,911,858×
87,465,579×
74,515,860×
71,161,511×
68,419,488×
72,040,737×
84,895,791×
94,631,278×
101,163,320×
117,130,118×
122,522,228×
123,221,703×
130,305,146×
119,395,230×
103,853,000×
90,084,890×
81,129,233×
84,748,381×
85,014,116×
70,670,203×
71,951,806×
69,804,023×
77,227,178×
91,889,266×
81,847,990×
81,026,649×
74,744,179×
99,599,166×
89,966,981×
82,347,017×
76,037,820×
68,667,190×
69,995,958×
73,694,421×
86,999,700×
69,964,145×
59,281,509×
62,918,950×
65,618,516×
61,648,926×
54,339,437×
65,959,715×
72,384,668×
44,973,073×
46,555,138×
52,649,989×
60,054,771×
51,630,279×
48,075,509×
44,863,883×
48,172,561×
43,065,215×
31,279,365×
26,357,784×
20,329,324×
19,231,669×
26,218,563×
26,618,932×
25,592,314×
26,637,884×
27,496,094×
24,018,037×
19,780,748×
15,954,982×
19,651,021×
24,110,244×
27,128,558×
29,001,764×
16,014,035×
18,062,086×
15,191,879×
10,258,028×
9,421,353×
7,722,545×
8,524,709×
8,665,430×
7,441,726×
8,929,702×
9,371,634×
10,417,197×
18,980,080×
11,118,742×
9,735,168×
11,022,501×
10,377,888×
12,430,189×
22,023,772×
24,255,614×
26,574,414×
24,514,039×
20,311,259×
18,999,839×
14,836,413×
14,993,597×
9,543,967×
8,409,295×
4,491,474×
4,274,425×
5,481,081×
6,905,637×
5,651,124×
4,634,595×
6,529,905×
3,701,542×
1,804,135×
1,132,952×
545,704×
228,413×
761,759×
3,021,894×
1,029,429×
1,011,680×
210,986×
127,312×
240,207×
993,804×
2,910,716×
158,988×
30,888×