Base 24: Iteration Frequencies: Full Cycle

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
Average Steps
Full Cycle
1.96 step
avg
9.47 step
avg
7.06 step
avg
16.21 step
avg
9.81 step
avg
30.05 step
avg
23.12 step
avg
60.00 step
avg
24.51 step
avg
88.35 step
avg
34.48 step
avg
120.61 step
avg
25.74 step
avg
52.50 step
avg
Step Frequency
Full Cycle
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23×
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24×
27×
18×






111×
114×
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179×
154×
306×
298×
286×
270×
250×
226×
198×
166×
130×
90×
46×
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23×










957×
1,439×
3,364×
5,352×
2,852×
1,672×
1,068×
360×
462×
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671×
1,758×
2,018×
3,536×
6,670×
11,600×
10,372×
8,658×
9,220×
9,580×
11,666×
9,796×
7,668×
3,812×
1,208×
46×
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179×


1,036×
1,828×
3,930×
6,210×
6,640×
8,828×
8,073×
10,318×
12,381×
7,910×
8,878×
7,642×
6,886×
2,900×
1,312×
7,540×
12,299×
14,274×
9,788×
9,575×
7,646×
13,570×
19,071×
14,633×
14,564×
16,690×
19,590×
20,410×
19,550×
10,897×
9,513×
14,975×
15,620×
9,420×
8,874×
11,750×
8,483×
13,546×
13,186×
5,533×
5,752×
7,261×
6,738×
7,896×
7,104×
4,494×
7,498×
4,538×
2,392×
3,092×
758×
1,362×
186×
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2,081×
7,456×
20,368×
27,342×
42,976×
64,356×
58,178×
35,220×
11,438×
310×








35,946×
70,730×
106,930×
135,456×
198,916×
262,064×
301,614×
272,486×
197,888×
97,058×
47,036×
22,626×
13,904×
3,420×
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1,175×
3,102×

















15,460×
53,712×
75,246×
94,976×
186,585×
175,533×
175,679×
120,291×
92,259×
137,990×
158,807×
171,130×
188,103×
166,112×
140,049×
147,872×
160,884×
162,456×
131,741×
128,899×
139,327×
139,828×
127,508×
130,412×
139,950×
159,038×
151,690×
114,183×
89,861×
100,646×
127,268×
99,292×
70,973×
58,040×
69,156×
69,693×
91,773×
57,116×
29,241×
27,263×
46,553×
50,779×
55,045×
66,540×
51,997×
55,580×
44,571×
46,660×
69,102×
73,328×
89,521×
98,432×
104,206×
97,069×
77,245×
60,479×
43,301×
51,959×
57,295×
48,560×
35,370×
40,376×
46,937×
31,668×
17,145×
25,112×
42,018×
36,560×
43,949×
38,961×
25,969×
12,491×
7,074×
19,464×
35,429×
32,795×
29,102×
28,624×
44,459×
58,308×
41,937×
45,754×
56,877×
73,433×
46,450×
51,102×
56,381×
58,900×
89,248×
79,482×
93,387×
72,895×
68,338×
46,197×
27,097×
25,408×
23,451×
29,378×
50,257×
46,181×
27,298×
29,171×
34,158×
42,459×
25,737×
15,728×
8,252×
3,416×
0s:
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5,579×
26,554×
79,680×
183,188×
379,762×
513,938×
555,318×
614,102×
797,044×
740,936×
1,088,950×
1,160,234×
1,315,678×
1,421,422×
1,449,338×
985,242×
493,112×
370,886×
496,770×
376,468×
382,468×
180,162×
159,468×
299,986×
348,752×
199,166×
198,446×
497,178×
791,566×
993,168×
1,287,050×
1,596,446×
1,509,618×
1,472,030×
923,564×
710,252×
465,556×
464,148×
524,444×
458,002×
309,926×
282,598×
331,080×
228,924×
151,736×
106,118×
89,260×
23,334×
10,152×
0s:
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2,519×
22,966×
35,039×
33,878×
34,094×
43,928×
44,102×
11,962×
2,772×
2,986×
9,668×
10,544×
15,134×
34,176×
168,600×
265,356×
248,160×
218,940×
173,067×
222,959×
283,345×
277,986×
346,548×
352,509×
256,819×
247,780×
223,849×
217,887×
234,393×
300,782×
265,696×
129,376×
39,638×
33,688×
17,406×
1,966×
3,371×
696×

54,285×
412,366×
620,442×
496,503×
479,307×
502,023×
530,046×
733,008×
699,305×
615,734×
517,770×
538,214×
615,937×
628,879×
565,592×
549,255×
473,714×
443,521×
481,443×
392,033×
378,392×
509,018×
613,024×
721,763×
839,312×
934,017×
848,616×
1,022,334×
910,570×
1,004,969×
1,019,657×
962,843×
944,001×
957,692×
888,567×
1,035,014×
693,921×
672,930×
807,935×
1,010,574×
958,466×
1,066,525×
2,005,737×
2,344,982×
1,983,586×
2,135,144×
1,876,668×
1,580,705×
1,440,687×
1,395,645×
1,324,505×
1,264,563×
1,210,828×
1,134,614×
1,244,009×
1,618,455×
1,637,208×
1,309,986×
1,399,605×
1,259,018×
1,274,477×
1,181,345×
1,220,724×
1,223,226×
1,333,389×
944,202×
770,096×
828,584×
921,351×
1,218,493×
1,338,860×
1,203,117×
885,864×
648,318×
629,558×
565,181×
712,407×
866,528×
760,043×
541,989×
542,378×
642,240×
751,481×
443,297×
291,110×
350,473×
417,180×
333,454×
285,396×
186,665×
281,546×
237,295×
267,964×
303,730×
381,630×
425,947×
318,607×
388,968×
411,922×
393,361×
291,737×
236,672×
326,123×
211,063×
254,919×
242,777×
213,153×
164,828×
160,526×
129,436×
110,014×
167,916×
244,089×
247,924×
140,157×
86,288×
56,867×
63,097×
61,162×
76,881×
84,823×
64,886×
28,116×
18,514×
1,316×
844×
1,664×
1,184×
528×
1,092×
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13,675×
112,480×
497,470×
672,742×
684,628×
425,602×
102,246×
25,906×
6,472×
1,924×
104,490×
635,138×
1,393,908×
1,479,378×
1,897,792×
3,479,850×
5,351,216×
6,366,572×
7,349,632×
9,949,024×
11,874,562×
13,589,494×
10,042,520×
7,379,080×
7,590,354×
8,935,012×
8,958,860×
8,785,260×
7,687,102×
8,196,578×
7,486,228×
9,315,740×
6,269,422×
4,288,588×
4,103,502×
5,187,732×
5,318,870×
4,745,042×
4,763,432×
4,492,504×
4,310,610×
4,122,406×
4,944,370×
6,646,082×
9,315,226×
9,367,182×
9,756,346×
9,589,554×
9,552,438×
8,268,120×
5,593,346×
4,183,034×
3,261,032×
2,886,888×
2,344,472×
1,442,824×
689,470×
163,238×
86,616×
14,478×
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179×









39,532×
866,894×
2,007,697×
1,653,134×
2,165,735×
2,809,579×
4,713,968×
6,770,786×
5,900,174×
5,467,942×
4,954,073×
4,518,072×
3,558,565×
3,509,344×
2,987,624×
2,890,124×
3,552,469×
3,909,131×
4,982,584×
3,831,258×
3,043,796×
2,717,969×
2,809,149×
3,844,586×
3,967,173×
3,636,563×
4,664,832×
4,093,308×
4,989,632×
4,891,459×
5,696,421×
6,394,137×
6,983,867×
6,811,855×
6,552,000×
6,635,629×
7,247,807×
6,453,047×
5,329,386×
4,648,294×
4,931,229×
4,327,435×
5,906,896×
6,677,954×
7,574,645×
6,266,699×
5,867,324×
3,827,401×
4,660,243×
5,728,619×
5,670,595×
5,042,701×
5,034,194×
4,474,692×
4,029,193×
3,260,416×
3,472,056×
3,487,081×
2,447,770×
2,501,877×
2,102,258×
1,806,958×
1,526,348×
1,691,286×
2,220,510×
1,505,185×
1,106,012×
1,249,151×
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1,175×
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13,150,336×
9,782,808×
7,345,784×
4,544,490×
2,427,308×
1,913,822×
443,638×
18,340×
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18,281×
104,388×
76,266×

15,696×
469,336×
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2,364,916×
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4,111,459×
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61,207,355×
67,457,852×
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129,929,550×
135,863,209×
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120,890,392×
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113,500,513×
101,697,333×
94,388,746×
93,849,937×
99,056,142×
103,556,328×
113,701,790×
110,986,196×
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122,667,890×
119,718,532×
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91,780,428×
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48,258,490×
38,541,339×
38,601,455×
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8,210×