Base 17: 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 20
Average Steps
Cycle Start
0.94 step
avg
2.05 step
avg
4.18 step
avg
1.98 step
avg
5.63 step
avg
15.49 step
avg
10.65 step
avg
12.46 step
avg
15.19 step
avg
17.88 step
avg
20.29 step
avg
14.47 step
avg
12.88 step
avg
15.28 step
avg
32.33 step
avg
20.31 step
avg
12.78 step
avg
18.76 step
avg
14.71 step
avg
28.36 step
avg
Step Frequency
Cycle Start
0s:
1s:

16×
0s:
1s:
2s:
3s:

50×
36×
64×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:

177×
77×
152×
142×
128×
110×
88×
62×
32×
0s:
1s:
2s:
3s:
4s:

1,024×
2,964×
776×
80×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:

1,000×
1,550×
1,699×
3,487×
3,711×
2,148×
1,200×
1,281×
2,022×
1,634×
616×
0s:
1s:
2s:
3s:
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5s:
6s:
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36s:
37s:
38s:
39s:
40s:

176×
769×
1,691×
1,329×
1,533×
3,740×
3,400×
5,283×
3,432×
3,622×
3,478×
1,951×
3,164×
3,569×
5,483×
3,331×
3,588×
3,250×
2,549×
2,155×
2,173×
2,491×
2,182×
749×
193×
416×
782×
1,153×
776×
349×
259×
351×
1,094×
659×
392×
505×
257×
414×
1,128×
796×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
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18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:

4,328×
6,808×
8,664×
13,745×
17,654×
20,957×
26,773×
30,440×
18,603×
8,359×
5,821×
5,757×
10,067×
8,233×
6,881×
6,358×
5,232×
3,901×
3,064×
2,247×
2,212×
1,516×
3,599×
5,453×
8,125×
6,440×
3,425×
336×
158×
0s:
1s:
2s:
3s:
4s:
5s:
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25s:
26s:
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28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:

3,506×
13,548×
34,993×
56,831×
50,067×
31,832×
36,264×
41,885×
23,777×
22,015×
25,524×
32,983×
34,804×
23,436×
32,398×
38,564×
43,542×
20,256×
25,548×
39,992×
33,031×
13,848×
22,839×
15,928×
5,294×
6,085×
3,226×
1,386×
808×
353×
228×
272×
193×
124×
90×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:

14,984×
46,561×
62,522×
73,263×
92,402×
101,164×
93,275×
89,814×
91,134×
103,669×
145,030×
113,831×
97,895×
74,278×
48,417×
61,767×
37,532×
29,033×
24,327×
33,547×
31,248×
54,807×
55,294×
58,347×
56,538×
46,196×
37,180×
25,178×
18,690×
26,752×
46,142×
39,349×
29,150×
17,290×
15,667×
14,765×
22,266×
9,849×
3,197×
624×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
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43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:

12,854×
67,188×
243,792×
284,250×
175,030×
144,834×
165,864×
110,929×
67,408×
88,554×
167,309×
143,763×
148,417×
167,904×
185,402×
296,572×
214,131×
340,547×
227,220×
203,492×
137,525×
145,424×
193,913×
192,759×
176,362×
130,171×
98,724×
69,523×
90,703×
67,386×
51,853×
43,595×
39,054×
31,259×
18,075×
23,321×
42,517×
26,977×
15,569×
5,486×
1,395×
6,607×
40,918×
40,568×
40,405×
43,503×
34,426×
22,164×
17,473×
6,160×
1,508×
631×
170×
150×
0s:
1s:
2s:
3s:
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33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:

35,710×
132,638×
216,778×
234,966×
281,704×
252,305×
272,472×
376,241×
379,961×
317,994×
283,159×
359,268×
392,026×
427,878×
356,138×
420,075×
629,206×
523,281×
455,687×
409,348×
403,852×
389,368×
400,850×
438,495×
335,159×
352,208×
373,384×
396,950×
464,504×
547,754×
413,801×
295,435×
257,752×
253,396×
220,739×
201,579×
146,117×
92,768×
92,371×
120,836×
50,367×
25,498×
7,268×
608×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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37s:
38s:
39s:
40s:
41s:
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46s:
47s:
48s:

22,891×
176,593×
786,516×
1,297,925×
1,642,251×
2,010,500×
1,903,135×
2,152,168×
1,681,831×
1,446,607×
1,021,342×
1,722,524×
1,830,555×
1,224,953×
946,412×
838,150×
700,829×
650,675×
682,869×
650,915×
586,014×
331,676×
535,606×
413,024×
360,150×
225,965×
411,090×
294,297×
328,449×
885,315×
624,337×
635,139×
384,960×
299,245×
143,202×
105,738×
56,006×
102,925×
103,209×
127,298×
48,070×
21,395×
7,296×
112×
1,444×
39×
46×
66×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:

37,168×
300,692×
954,158×
1,972,378×
2,635,850×
2,660,869×
3,726,554×
3,891,818×
4,501,441×
4,657,859×
5,088,673×
5,254,270×
4,593,744×
4,296,519×
3,239,280×
2,608,126×
3,040,141×
3,040,197×
2,598,659×
1,948,576×
1,606,760×
1,289,279×
901,567×
618,902×
436,214×
503,463×
419,555×
258,140×
155,913×
146,455×
132,030×
81,690×
68,488×
97,561×
82,305×
11,572×
6,544×
504×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
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9s:
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38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:

38,211×
521,285×
3,173,915×
8,960,092×
8,621,080×
5,315,103×
7,262,554×
7,770,863×
7,575,919×
6,931,647×
6,059,704×
4,106,301×
4,435,238×
4,505,356×
5,166,202×
4,518,594×
5,200,500×
4,148,990×
4,723,864×
6,953,200×
3,956,666×
4,115,724×
4,029,033×
3,386,195×
3,817,928×
2,541,182×
1,873,545×
2,676,350×
2,973,608×
1,837,589×
1,446,668×
1,029,318×
577,514×
992,864×
774,826×
494,977×
255,244×
238,056×
242,016×
602,425×
397,031×
211,848×
270,479×
428,206×
154,588×
60,361×
45,025×
3,914×
876×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
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61s:
62s:
63s:

22,696×
291,180×
773,537×
1,063,801×
763,090×
1,916,383×
1,592,837×
1,175,668×
1,430,200×
2,158,822×
2,386,898×
3,159,033×
3,905,646×
3,794,334×
3,390,028×
3,598,769×
4,063,847×
3,837,820×
4,150,023×
5,042,918×
4,289,442×
4,514,087×
5,717,530×
5,960,163×
7,037,883×
8,468,693×
8,993,743×
9,395,628×
9,570,167×
10,855,450×
9,896,418×
9,742,396×
10,461,330×
10,973,003×
11,890,307×
12,327,566×
13,265,369×
12,036,894×
10,827,959×
9,302,051×
7,530,328×
6,994,156×
6,458,953×
4,708,957×
4,617,967×
4,635,995×
3,886,112×
3,144,505×
3,069,121×
3,581,744×
3,301,181×
2,726,484×
2,490,537×
2,348,185×
2,620,499×
1,587,606×
967,664×
769,785×
660,605×
264,853×
93,446×
33,350×
4,552×
0s:
1s:
2s:
3s:
4s:
5s:
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48s:
49s:
50s:

51,511×
808,082×
6,260,295×
21,664,287×
19,442,016×
15,894,749×
14,851,001×
14,369,566×
15,815,532×
14,099,167×
14,208,047×
13,434,284×
20,512,956×
22,103,945×
20,666,240×
25,060,217×
22,924,549×
21,931,863×
23,415,521×
15,712,631×
15,216,541×
17,503,664×
16,475,268×
18,029,530×
13,851,570×
14,660,866×
23,858,718×
20,561,776×
12,038,934×
12,096,330×
13,323,887×
15,404,712×
14,650,066×
8,368,089×
6,444,850×
5,788,583×
8,489,161×
12,593,430×
8,713,745×
4,967,936×
3,094,860×
3,156,861×
2,571,774×
2,282,951×
607,842×
828,730×
591,719×
1,453,591×
214,720×
13,226×
0s:
1s:
2s:
3s:
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41s:
42s:
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44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:

225,304×
4,501,840×
15,125,235×
29,927,279×
46,409,709×
74,743,599×
73,621,883×
77,742,725×
88,081,470×
91,589,621×
76,563,682×
78,396,459×
78,850,986×
75,516,095×
58,799,297×
45,777,630×
34,396,723×
29,925,288×
25,097,667×
22,156,123×
17,542,356×
16,043,219×
18,096,075×
15,501,760×
11,835,072×
10,118,959×
6,999,288×
6,638,429×
4,463,636×
4,123,718×
4,612,028×
4,730,261×
4,556,687×
1,762,727×
1,400,686×
1,990,760×
1,718,968×
1,160,484×
1,461,446×
969,085×
891,248×
560,784×
650,516×
383,764×
178,164×
193,220×
413,588×
239,788×
89,400×
27,808×
570×
0s:
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63s:
64s:

166,260×
4,375,378×
34,521,848×
113,237,339×
133,340,669×
99,041,386×
82,858,611×
77,876,021×
66,106,338×
81,661,760×
83,916,692×
95,175,251×
80,581,699×
48,497,511×
46,825,452×
46,499,058×
55,261,046×
56,984,783×
65,724,708×
56,673,557×
54,984,611×
69,545,050×
63,545,635×
59,309,787×
50,296,208×
58,869,679×
58,862,595×
44,878,095×
35,841,746×
38,537,177×
22,509,991×
20,505,139×
24,036,209×
22,078,432×
12,465,672×
14,395,929×
8,284,071×
16,715,201×
20,186,446×
20,640,478×
13,504,781×
10,867,899×
5,091,206×
7,239,055×
8,642,199×
17,568,312×
19,789,438×
8,928,281×
15,381,866×
15,175,982×
10,412,082×
6,743,266×
8,595,511×
3,919,304×
1,780,068×
1,163,846×
2,154,750×
1,002,366×
80,947×
37,043×
69,293×
208×
150×
58×
0s:
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39s:

237,336×
6,071,796×
26,142,980×
62,177,085×
88,188,662×
164,531,629×
206,248,637×
210,552,257×
235,011,165×
286,598,910×
246,612,437×
223,304,351×
213,539,700×
209,409,905×
226,143,134×
197,205,782×
205,238,329×
166,713,368×
143,167,572×
118,006,826×
111,844,719×
94,752,020×
96,671,661×
93,111,961×
96,848,285×
90,642,988×
75,630,137×
54,372,964×
37,918,357×
27,770,686×
19,173,767×
10,317,955×
6,314,624×
4,315,692×
2,963,945×
1,424,944×
613,349×
131,969×
7,065×
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232,915×
10,169,410×
95,243,956×
429,503,701×
408,220,164×
347,836,929×
185,814,244×
150,118,896×
149,404,165×
208,071,943×
183,546,462×
234,790,024×
158,699,163×
181,363,387×
131,807,889×
130,358,357×
117,280,080×
131,635,909×
133,879,088×
117,922,390×
104,979,113×
141,924,698×
142,844,489×
112,537,050×
139,703,865×
67,284,391×
109,558,299×
64,967,921×
91,198,946×
129,313,708×
143,257,709×
109,672,998×
75,851,093×
74,467,199×
73,635,488×
58,602,740×
58,939,449×
60,743,369×
52,910,153×
63,475,764×
63,160,242×
32,675,858×
23,905,311×
20,706,792×
29,457,203×
61,821,679×
72,412,956×
72,466,275×
101,254,673×
120,575,407×
80,204,091×
75,875,755×
51,469,251×
42,330,162×
55,922,914×
44,360,211×
31,543,601×
45,041,291×
56,962,164×
28,181,560×
20,429,685×
29,633,933×
52,979,423×
51,571,488×
45,557,148×
56,879,161×
40,516,987×
31,570,542×
28,608,483×
20,579,131×
19,047,476×
14,098,990×
11,654,414×
9,891,174×
9,258,939×
6,288,731×
3,436,915×
8,000,773×
5,870,513×
4,474,552×
20,581,603×
5,580,013×
4,295,738×
20,730,143×
101,667,641×
29,390,491×
10,908,725×
6,754,722×
28,613,569×
31,773,837×
40,765,711×
9,590,046×
7,831,363×
9,289,767×
6,077,716×
5,210,427×
1,721,337×
2,113,031×
2,248,891×
177,604×
102,286×
2,376×
1,704×