Base 60: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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
Average Steps
Full Cycle		1.98 step
avg		30.52 step
avg		13.89 step
avg		8.01 step
avg		15.96 step
avg		103.41 step
avg		28.49 step
avg		145.65 step
avg
Step Frequency
Full Cycle
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0×
1×
59×
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0×
1×
59×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
15×
885×
870×
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0×
1×
989×
928×
1,854×
1,846×
1,834×
1,818×
1,798×
1,774×
1,746×
1,714×
1,678×
1,638×
1,594×
1,546×
1,494×
1,438×
1,378×
1,314×
1,246×
1,174×
1,098×
1,018×
934×
846×
754×
658×
558×
454×
346×
234×
118×
0s:
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0×
1×
659×
2,548×
7,824×
37,008×
76,608×
68,000×
250,918×
43,230×
32,769×
56,126×
5,736×
3,004×
5,590×
5,644×
0s:
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0×
1×
8,879×
16,092×
22,880×
48,482×
79,380×
139,350×
173,532×
257,888×
249,910×
434,280×
494,610×
579,884×
491,728×
635,960×
508,176×
580,436×
509,082×
516,970×
411,658×
393,194×
302,308×
252,210×
194,968×
150,380×
104,454×
50,426×
15,262×
2,014×
118×
0s:
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0×
1×
989×
0×
3,388×
19,334×
19,712×
16,234×
29,004×
62,316×
108,644×
161,056×
123,120×
70,656×
53,798×
60,668×
70,662×
44,695×
19,158×
6,156×
6,402×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
109,787×
285,750×
259,889×
402,255×
519,000×
632,121×
455,447×
476,779×
538,930×
579,243×
504,956×
419,281×
418,163×
404,959×
411,783×
383,325×
579,054×
796,876×
731,824×
684,314×
787,582×
860,903×
1,014,994×
1,059,274×
1,189,684×
1,079,125×
1,001,164×
892,498×
806,089×
722,138×
840,146×
692,470×
746,175×
708,802×
711,820×
852,531×
863,336×
875,217×
873,474×
974,439×
1,043,094×
1,014,633×
964,289×
1,060,245×
1,194,645×
1,129,811×
1,120,765×
1,058,897×
1,036,200×
1,132,408×
1,097,525×
1,084,643×
1,108,030×
1,163,992×
1,274,622×
1,308,866×
1,261,127×
1,281,839×
1,110,685×
1,272,596×
1,156,888×
1,053,183×
802,398×
1,042,391×
978,403×
952,924×
1,077,229×
1,045,290×
965,721×
777,007×
817,510×
745,294×
874,380×
776,856×
784,819×
685,266×
783,577×
762,490×
854,344×
709,595×
592,915×
564,991×
412,240×
460,818×
429,033×
409,720×
434,451×
412,119×
346,657×
398,014×
401,615×
410,757×
333,526×
356,635×
259,917×
331,067×
304,787×
323,290×
392,476×
379,571×
349,598×
444,109×
357,244×
318,744×
276,625×
277,392×
292,958×
224,017×
201,124×
232,057×
132,553×
110,800×
159,402×
155,394×
203,202×
256,159×
274,999×
302,326×
298,911×
292,562×
340,287×
256,487×
212,158×
102,542×
54,808×
49,972×
39,022×
42,762×
0s:
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0×
1×
61,499×
225,616×
752,576×
1,256,590×
2,099,938×
2,468,284×
4,076,546×
5,547,710×
6,547,486×
8,422,616×
8,109,012×
11,306,910×
12,172,502×
12,440,588×
13,267,000×
8,641,382×
4,002,706×
1,746,846×
2,194,826×
3,360,418×
6,474,584×
9,943,718×
15,866,364×
22,069,308×
28,001,400×
39,646,368×
51,144,586×
62,005,444×
67,569,036×
74,520,620×
63,741,232×
57,990,198×
51,486,714×
43,489,988×
33,509,382×
18,603,392×
10,562,510×
6,730,986×
4,036,714×
1,607,744×
1,046,204×
33,440×
8,456×
0s:
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0×
1×
16,859×
48,534×
237,440×
1,841,264×
2,660,532×
2,480,632×
3,160,428×
3,671,247×
3,704,169×
3,457,341×
3,717,700×
3,985,058×
4,052,956×
4,217,373×
4,612,896×
4,959,126×
7,042,610×
7,302,681×
7,545,703×
7,216,970×
7,540,332×
8,166,242×
10,630,947×
12,154,807×
9,874,544×
8,207,322×
7,694,385×
8,388,747×
8,850,804×
9,312,196×
11,696,518×
12,383,342×
12,286,239×
11,226,234×
11,925,330×
11,987,918×
14,921,993×
15,497,408×
14,715,656×
17,560,853×
17,221,497×
14,948,953×
15,921,661×
16,698,459×
17,529,089×
22,930,951×
22,286,118×
21,999,246×
25,816,574×
26,898,885×
24,005,718×
21,064,293×
21,845,303×
23,376,753×
24,507,768×
26,109,461×
26,466,001×
27,316,532×
25,924,380×
27,155,300×
23,794,342×
24,255,197×
26,596,741×
30,313,475×
29,660,824×
26,949,908×
24,182,195×
25,274,721×
26,148,162×
28,827,413×
31,674,574×
32,033,775×
30,763,584×
26,934,489×
28,384,031×
26,975,124×
27,469,838×
30,027,369×
30,709,549×
31,487,177×
35,912,542×
37,787,328×
39,496,359×
41,585,133×
42,142,824×
41,967,093×
43,361,327×
43,291,694×
40,105,075×
41,513,595×
40,156,252×
37,735,588×
34,574,679×
34,574,961×
32,032,588×
34,083,182×
34,530,376×
36,709,114×
37,921,507×
36,044,513×
34,542,246×
33,041,587×
30,182,380×
32,205,747×
29,905,087×
31,471,554×
32,931,880×
32,340,282×
32,279,574×
31,081,948×
29,232,823×
30,579,461×
29,595,547×
29,054,418×
31,132,050×
32,297,104×
30,323,647×
30,150,050×
31,237,541×
33,699,156×
32,814,358×
30,254,470×
31,221,929×
29,771,439×
28,250,832×
27,765,391×
27,176,742×
28,042,193×
28,796,453×
27,489,274×
32,387,930×
37,172,732×
38,260,937×
38,183,735×
38,413,960×
39,526,462×
38,906,476×
37,260,107×
37,071,739×
35,804,147×
34,827,696×
33,539,389×
34,409,964×
36,705,695×
38,922,696×
36,783,617×
36,640,184×
37,920,575×
34,328,404×
33,220,805×
32,759,220×
31,136,974×
31,145,176×
33,870,457×
32,525,874×
30,636,446×
32,121,788×
31,778,211×
29,443,582×
29,111,070×
33,971,168×
38,887,133×
40,659,449×
37,753,271×
34,285,714×
32,749,394×
25,905,904×
23,223,711×
20,569,372×
20,007,456×
21,603,182×
21,402,160×
23,371,072×
22,675,563×
22,661,726×
22,393,342×
21,490,513×
23,882,284×
20,745,644×
23,379,390×
22,606,871×
22,292,750×
21,346,818×
20,578,666×
21,949,073×
22,413,250×
21,751,945×
20,189,012×
19,728,393×
19,779,179×
20,490,877×
20,744,737×
18,948,164×
19,165,955×
20,083,925×
16,972,767×
19,542,830×
19,326,079×
18,503,822×
17,830,243×
17,930,915×
16,374,471×
15,211,969×
14,819,135×
15,834,432×
17,233,247×
17,320,525×
20,908,741×
23,207,236×
22,144,530×
22,208,288×
22,000,018×
22,593,670×
25,135,900×
29,097,158×
26,695,295×
22,992,109×
23,451,706×
22,922,959×
24,960,609×
25,468,855×
24,253,984×
25,628,695×
26,002,797×
22,609,897×
22,003,503×
23,112,976×
23,823,993×
24,603,216×
23,166,469×
21,270,968×
21,669,478×
22,485,716×
21,623,057×
21,971,357×
17,553,909×
15,927,821×
14,706,772×
13,790,315×
14,311,865×
15,071,556×
14,788,443×
15,303,937×
15,666,670×
13,325,369×
13,791,410×
15,077,896×
17,462,095×
18,332,713×
14,933,929×
13,936,910×
14,543,270×
13,832,190×
11,707,807×
11,207,818×
12,869,282×
11,697,417×
10,487,514×
10,765,155×
12,164,996×
12,856,280×
12,950,778×
12,531,581×
9,788,497×
8,537,012×
7,089,608×
7,878,199×
8,577,345×
8,034,715×
6,754,918×
6,207,657×
6,836,739×
6,824,003×
7,456,118×
5,631,440×
6,415,700×
5,843,004×
7,568,141×
6,817,113×
7,246,501×
6,608,673×
7,887,493×
7,720,407×
9,009,015×
9,996,190×
11,027,361×
8,728,241×
8,386,634×
9,158,225×
8,965,542×
7,755,720×
7,177,259×
6,716,533×
7,359,725×
5,583,425×
4,170,810×
4,250,035×
4,269,624×
3,490,577×
2,769,926×
3,765,795×
3,981,462×
2,665,776×
2,258,115×
2,427,772×
2,249,045×
1,562,931×
1,638,562×
2,397,364×
1,558,451×
1,413,426×
965,874×
573,304×
646,379×
431,971×
560,382×
892,008×
1,477,155×
2,057,673×
2,463,158×
1,790,900×
1,143,432×
1,338,868×
1,238,350×
1,381,955×
1,494,211×
1,501,453×
2,135,078×
2,074,510×
1,855,451×
2,267,858×
1,925,804×
1,699,191×
942,546×
921,659×
1,463,146×
2,215,765×
1,937,495×
2,393,155×
2,367,466×
1,531,796×
1,235,114×
2,186,860×
1,766,362×
2,238,923×
1,481,868×
1,865,211×
1,288,121×
1,037,950×
1,219,700×
1,130,663×
1,961,410×
2,170,792×
2,221,532×
1,331,758×
1,329,164×
1,367,678×
1,470,563×
1,501,645×
1,852,913×
1,700,308×
1,932,581×
1,437,418×
1,296,735×
826,565×
1,104,264×
835,016×
543,888×
447,682×
448,097×
158,379×
23,126×
108,990×
227,094×
93,904×
92,662×
36,808×
205,428×
237,342×
77,962×
151,057×
185,099×
247,033×
159,398×
129,748×
4,632×
3,216×