Base 18: Iteration Frequencies: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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 11 12 13 14 15 16 17 18 19
Average Steps
Cycle Start
0.94 step
avg
1.39 step
avg
4.89 step
avg
3.72 step
avg
7.76 step
avg
10.65 step
avg
10.65 step
avg
10.77 step
avg
10.47 step
avg
33.78 step
avg
12.68 step
avg
14.90 step
avg
15.12 step
avg
19.76 step
avg
12.10 step
avg
18.99 step
avg
14.69 step
avg
18.16 step
avg
21.42 step
avg
Step Frequency
Cycle Start
0s:
1s:

17×
0s:
1s:
2s:

93×
72×
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1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:

107×
88×
174×
166×
154×
138×
118×
94×
66×
34×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:

297×
588×
2,376×
1,067×
881×
441×
334×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:

561×
742×
1,218×
2,006×
2,486×
2,502×
2,366×
1,598×
2,708×
4,516×
3,660×
1,664×
306×
0s:
1s:
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3s:
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5s:
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30s:

3,662×
5,862×
8,814×
7,248×
7,085×
8,055×
8,801×
6,030×
3,331×
3,549×
2,816×
1,614×
1,436×
1,670×
2,288×
2,182×
1,032×
2,361×
2,771×
2,997×
3,293×
3,115×
3,011×
2,538×
2,177×
1,210×
236×
828×
652×
282×
0s:
1s:
2s:
3s:
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5s:
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8s:
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18s:
19s:

2,647×
4,752×
8,532×
10,978×
12,660×
8,040×
11,070×
16,670×
24,514×
38,200×
52,508×
54,156×
38,996×
22,490×
19,090×
13,008×
5,964×
1,794×
34×
0s:
1s:
2s:
3s:
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5s:
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41s:
42s:
43s:

15,945×
59,193×
63,203×
63,962×
73,097×
67,614×
69,030×
62,325×
56,840×
58,307×
68,960×
58,702×
53,592×
47,202×
39,623×
31,326×
28,070×
25,290×
26,419×
23,489×
18,395×
10,071×
10,259×
5,127×
2,302×
2,705×
3,892×
5,119×
2,946×
3,065×
3,824×
6,443×
1,798×
1,259×
3,058×
3,045×
2,459×
1,010×
786×
540×
250×
816×
216×
0s:
1s:
2s:
3s:
4s:
5s:
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21s:
22s:
23s:
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25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:

35,289×
102,154×
173,212×
214,180×
257,680×
314,620×
268,930×
163,236×
158,616×
125,860×
131,602×
126,578×
155,132×
138,066×
81,916×
67,778×
87,850×
126,916×
107,394×
66,576×
23,568×
14,088×
10,520×
18,468×
20,450×
27,564×
53,442×
34,302×
11,566×
4,842×
2,016×
138×
0s:
1s:
2s:
3s:
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83s:
84s:
85s:
86s:
87s:
88s:
89s:

9,490×
62,522×
49,986×
73,807×
91,893×
121,453×
144,739×
176,213×
184,513×
189,234×
188,608×
179,664×
185,512×
214,101×
191,342×
117,045×
118,053×
168,854×
201,991×
238,311×
233,740×
204,858×
185,542×
168,443×
178,925×
181,690×
152,800×
89,265×
47,542×
52,360×
59,911×
61,320×
60,322×
45,199×
66,168×
56,385×
63,728×
66,129×
56,850×
50,220×
40,458×
53,318×
77,639×
146,427×
145,721×
159,198×
188,781×
181,492×
175,703×
163,084×
149,755×
199,985×
202,040×
193,885×
132,506×
69,027×
37,993×
32,395×
25,570×
38,150×
54,775×
53,030×
49,041×
77,581×
92,471×
83,786×
50,150×
66,377×
70,421×
88,597×
51,442×
32,727×
36,246×
32,159×
21,480×
22,702×
14,475×
14,709×
19,998×
30,494×
13,761×
10,011×
12,481×
14,276×
8,960×
4,738×
4,494×
2,732×
315×
0s:
1s:
2s:
3s:
4s:
5s:
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28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:

49,177×
304,822×
683,294×
816,804×
1,076,418×
1,247,214×
1,288,300×
1,276,238×
1,316,340×
1,411,740×
1,543,812×
1,471,176×
1,252,596×
986,960×
695,188×
743,786×
712,494×
856,680×
591,886×
300,524×
214,150×
180,248×
218,184×
264,866×
235,104×
272,114×
326,854×
294,480×
243,172×
154,594×
89,996×
110,282×
68,422×
56,422×
70,112×
35,034×
13,912×
784×
0s:
1s:
2s:
3s:
4s:
5s:
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44s:
45s:
46s:

66,074×
827,345×
1,116,797×
1,494,351×
1,798,770×
1,936,864×
2,133,089×
2,120,351×
2,122,000×
2,236,475×
2,363,909×
2,513,636×
2,852,352×
2,961,900×
2,517,026×
2,383,140×
2,144,826×
2,161,679×
2,077,732×
2,076,805×
1,996,120×
1,653,141×
1,462,010×
1,208,690×
1,035,410×
955,089×
911,153×
750,205×
579,090×
366,985×
279,485×
197,175×
185,501×
103,669×
100,116×
47,289×
75,524×
31,937×
17,280×
5,026×
7,835×
2,440×
3,944×
6,569×
8,838×
292×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
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27s:
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31s:
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33s:
34s:
35s:
36s:
37s:

31,289×
359,918×
1,022,458×
1,480,852×
3,208,762×
4,323,354×
6,101,552×
7,170,670×
6,697,278×
6,750,340×
5,732,450×
5,981,388×
5,687,008×
5,809,702×
6,244,960×
5,572,770×
5,729,076×
4,805,744×
4,456,746×
4,712,132×
4,709,936×
3,836,252×
3,277,230×
2,869,042×
2,550,220×
2,094,456×
1,965,296×
1,597,158×
1,675,306×
1,377,640×
942,850×
529,618×
285,764×
133,202×
36,634×
642×
154×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
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60s:
61s:
62s:
63s:
64s:

119,788×
2,691,912×
3,509,165×
4,672,101×
5,729,248×
7,314,076×
8,831,131×
9,028,897×
9,310,041×
8,194,175×
7,030,848×
7,330,357×
9,293,925×
12,079,272×
13,975,391×
13,421,520×
13,249,788×
12,227,277×
10,316,787×
9,776,231×
9,986,695×
9,225,591×
7,767,198×
6,471,550×
5,329,977×
4,609,265×
3,261,810×
2,641,580×
2,628,502×
2,670,258×
2,200,019×
1,938,956×
1,779,978×
1,720,598×
1,307,733×
1,012,467×
1,099,515×
921,175×
1,231,297×
1,610,959×
2,088,523×
2,543,452×
2,362,360×
2,770,045×
2,649,060×
2,667,967×
2,891,317×
3,012,076×
1,956,207×
1,626,861×
820,046×
604,093×
507,120×
340,020×
225,839×
153,631×
112,633×
71,111×
104,482×
85,934×
43,869×
20,975×
5,386×
2,464×
0s:
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37s:
38s:

112,169×
2,212,850×
7,754,406×
14,751,470×
21,887,066×
37,918,532×
42,899,046×
50,283,358×
51,576,062×
54,340,930×
48,300,790×
40,613,714×
32,411,008×
23,813,362×
18,715,964×
13,758,746×
12,926,946×
9,662,678×
6,428,856×
6,728,306×
7,048,900×
5,953,704×
5,436,358×
7,483,586×
7,218,826×
6,561,380×
6,547,046×
4,667,876×
4,647,832×
4,253,056×
3,650,634×
2,313,052×
1,236,502×
780,692×
615,354×
186,134×
22,328×
3,200×
0s:
1s:
2s:
3s:
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66s:

347,900×
14,084,190×
20,852,221×
22,850,423×
24,197,884×
29,050,566×
37,066,407×
41,104,531×
47,508,481×
40,791,668×
31,455,795×
30,363,399×
37,601,021×
47,342,101×
57,074,470×
61,784,405×
63,816,496×
61,698,281×
54,250,539×
45,238,649×
45,463,833×
43,176,925×
35,473,315×
32,761,566×
28,731,799×
21,098,013×
14,290,865×
10,800,273×
8,738,613×
8,651,731×
7,560,226×
7,221,496×
7,274,075×
5,945,151×
4,570,920×
4,202,179×
4,281,414×
4,148,164×
3,735,737×
3,392,014×
4,609,266×
5,458,449×
5,756,851×
7,403,626×
8,414,681×
7,920,049×
8,571,334×
9,826,672×
7,585,621×
8,068,233×
5,619,104×
5,167,509×
4,331,521×
2,594,959×
2,077,512×
747,915×
277,386×
279,963×
272,539×
222,488×
301,724×
477,675×
548,624×
251,248×
15,309×
5,115×
0s:
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39s:
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41s:

142,763×
4,267,936×
18,015,588×
36,217,050×
55,264,896×
91,826,882×
110,739,052×
113,561,338×
122,893,204×
117,174,142×
105,223,586×
122,338,708×
137,255,298×
149,508,076×
154,838,848×
145,908,072×
140,592,246×
125,282,662×
101,903,398×
88,764,630×
67,368,544×
57,202,800×
48,140,374×
38,750,264×
28,020,632×
27,410,710×
32,138,716×
28,165,776×
24,057,602×
16,436,232×
9,668,178×
7,611,976×
2,498,020×
635,166×
534,810×
713,832×
1,411,904×
681,496×
401,828×
35,498×
3,486×
0s:
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1,001,432×
68,196,742×
111,881,933×
97,980,945×
82,955,933×
101,971,273×
121,363,291×
158,387,863×
190,726,849×
193,474,610×
160,903,149×
137,929,675×
150,349,812×
160,269,775×
185,758,875×
219,230,167×
247,374,091×
256,538,750×
234,772,995×
196,733,616×
183,450,844×
157,486,131×
127,015,339×
126,809,427×
122,337,293×
87,774,103×
69,844,946×
58,672,029×
44,553,931×
33,773,075×
24,570,702×
24,661,875×
22,221,240×
20,580,063×
17,021,396×
13,677,561×
15,589,339×
13,911,639×
11,017,187×
8,563,671×
9,581,586×
13,011,298×
16,751,721×
17,551,578×
24,422,945×
24,210,265×
25,241,689×
26,780,742×
23,140,580×
27,652,204×
21,810,234×
14,940,428×
10,541,661×
9,804,466×
5,433,672×
1,805,497×
1,018,352×
590,774×
955,008×
792,972×
121,176×
21,399×
28,553×
25,242×
40×
0s:
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100,857×
5,064,000×
27,684,754×
58,148,424×
123,223,520×
185,124,366×
243,353,304×
280,541,580×
299,328,774×
292,125,448×
260,161,454×
230,623,596×
243,550,948×
232,181,430×
226,712,370×
248,607,366×
291,054,328×
308,978,566×
321,864,594×
279,059,296×
252,615,946×
218,154,044×
245,972,890×
263,848,706×
286,453,676×
268,438,478×
240,843,548×
227,448,740×
226,899,894×
292,139,592×
326,614,322×
302,315,676×
269,779,272×
204,578,024×
165,788,220×
147,511,024×
121,138,076×
116,148,698×
82,603,528×
49,339,260×
35,500,014×
35,112,136×
31,476,858×
19,719,390×
7,360,552×
2,038,178×
157,642×
11,154×
86×