Base 62: Iteration Frequencies: Cycle Start

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
Cycle Start		0.98 step
avg		1.47 step
avg		13.26 step
avg		2.96 step
avg		13.07 step
avg		106.85 step
avg		17.49 step
avg		171.58 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
61×
0s:
1s:
2s:
17×
1,006×
930×
0s:
1s:
2s:
3s:
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23s:
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26s:
27s:
28s:
29s:
30s:
31s:
32s:
1×
1,053×
990×
1,978×
1,970×
1,958×
1,942×
1,922×
1,898×
1,870×
1,838×
1,802×
1,762×
1,718×
1,670×
1,618×
1,562×
1,502×
1,438×
1,370×
1,298×
1,222×
1,142×
1,058×
970×
878×
782×
682×
578×
470×
358×
242×
122×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
40,381×
107,310×
429,660×
49,126×
42,951×
4,599×
3,012×
0s:
1s:
2s:
3s:
4s:
5s:
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17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
1×
41,697×
49,938×
60,836×
138,200×
189,486×
301,072×
323,722×
483,260×
466,188×
718,044×
699,258×
786,962×
622,066×
745,400×
563,924×
556,544×
491,684×
432,764×
367,504×
278,350×
217,940×
139,644×
104,368×
77,080×
52,052×
26,966×
1,978×
0s:
1s:
2s:
3s:
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170s:
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172s:
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177s:
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214s:
215s:
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219s:
220s:
221s:
222s:
1×
610,973×
1,789,763×
886,839×
767,963×
851,723×
935,625×
760,373×
762,438×
856,642×
897,493×
1,055,737×
1,058,199×
948,323×
1,150,833×
1,092,717×
1,089,187×
1,169,497×
923,309×
840,726×
1,036,501×
953,987×
935,271×
953,798×
815,484×
929,723×
1,102,266×
886,362×
784,381×
666,581×
639,819×
519,717×
446,907×
626,294×
458,624×
349,820×
340,131×
283,702×
358,233×
349,746×
303,158×
274,155×
276,051×
286,953×
265,559×
201,799×
108,187×
164,437×
130,370×
191,563×
154,953×
247,044×
107,750×
79,439×
73,593×
86,734×
26,533×
16,254×
30,340×
33,483×
33,760×
38,336×
22,410×
69,578×
79,359×
71,416×
58,242×
81,052×
137,376×
117,634×
144,238×
132,175×
145,762×
145,724×
153,672×
178,922×
136,685×
118,354×
133,014×
52,772×
52,206×
99,910×
81,697×
38,671×
30,682×
26,596×
27,972×
43,453×
23,796×
26,762×
39,119×
33,394×
21,104×
31,614×
53,712×
48,378×
60,856×
59,027×
103,113×
130,781×
158,322×
110,132×
167,997×
155,019×
148,490×
146,429×
143,842×
138,007×
115,576×
128,464×
138,141×
76,008×
152,974×
209,842×
192,609×
201,731×
196,481×
249,817×
213,705×
184,790×
236,378×
202,239×
285,230×
397,026×
390,449×
368,031×
595,590×
667,793×
683,413×
744,604×
713,223×
752,069×
863,529×
827,971×
782,119×
757,267×
803,775×
846,859×
802,104×
743,056×
705,444×
815,281×
973,151×
911,229×
778,576×
958,089×
909,081×
959,077×
989,066×
924,001×
882,866×
980,034×
888,477×
890,500×
851,294×
840,869×
711,290×
664,022×
874,908×
872,378×
990,968×
1,006,325×
1,066,483×
1,125,273×
1,311,020×
1,171,001×
965,013×
969,419×
811,594×
720,730×
835,320×
734,069×
511,277×
600,909×
624,802×
779,359×
707,591×
868,500×
909,967×
742,296×
716,374×
786,903×
562,131×
513,044×
414,042×
367,852×
497,499×
493,360×
354,307×
259,710×
326,696×
369,495×
241,871×
275,922×
187,092×
126,900×
187,272×
129,876×
154,856×
182,335×
223,868×
196,383×
280,085×
130,189×
140,618×
178,270×
154,173×
162,512×
135,117×
142,510×
216,160×
337,301×
266,807×
231,616×
207,761×
166,169×
134,078×
175,340×
165,780×
192,844×
109,561×
104,464×
46,516×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
1×
274,765×
724,618×
1,732,300×
2,287,342×
3,430,172×
5,590,454×
8,269,332×
10,714,832×
15,693,398×
22,398,944×
29,525,172×
38,909,378×
49,081,202×
59,342,356×
63,137,802×
73,789,846×
77,369,884×
80,316,998×
81,908,204×
80,450,310×
71,498,430×
61,029,212×
48,793,168×
36,631,698×
20,374,842×
11,774,252×
7,350,800×
3,905,638×
1,816,034×
1,236,466×
76,662×
9,392×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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487s:
488s:
1×
1,255,357×
9,406,576×
10,924,212×
13,019,285×
18,218,278×
24,554,335×
33,986,661×
45,771,185×
35,095,219×
32,740,971×
30,624,707×
38,276,811×
42,131,841×
45,679,421×
52,899,032×
42,212,544×
49,943,441×
54,082,934×
69,020,421×
72,032,719×
65,917,762×
68,839,090×
66,660,411×
70,565,052×
71,754,807×
73,578,893×
71,397,587×
56,773,606×
54,726,658×
57,041,467×
59,683,235×
55,178,626×
57,780,083×
56,202,589×
58,690,497×
57,022,886×
57,931,966×
58,585,599×
56,912,846×
51,175,921×
49,135,138×
45,907,896×
48,310,717×
52,092,179×
48,476,052×
45,015,757×
40,595,075×
37,033,074×
31,270,578×
31,833,182×
34,108,594×
32,606,513×
31,428,081×
32,676,061×
30,898,848×
34,376,162×
32,163,030×
30,286,879×
29,282,698×
25,639,760×
23,778,522×
26,144,680×
22,353,959×
21,666,366×
25,728,243×
26,425,973×
24,127,264×
20,606,574×
19,562,202×
17,237,007×
17,202,237×
19,051,345×
15,500,343×
14,463,308×
15,261,626×
15,938,753×
15,040,189×
15,181,523×
16,498,104×
12,394,503×
9,758,498×
10,935,868×
12,232,024×
12,855,113×
11,477,157×
13,712,185×
15,850,062×
15,600,377×
13,791,554×
12,936,350×
15,076,561×
15,125,979×
17,182,270×
17,678,524×
14,526,384×
17,746,942×
18,905,172×
19,114,941×
22,765,580×
19,907,752×
17,185,864×
18,036,973×
18,078,832×
17,349,719×
20,268,199×
21,625,797×
22,672,496×
26,498,504×
26,070,273×
24,203,715×
21,089,127×
20,725,294×
20,062,083×
22,087,634×
25,334,248×
23,827,993×
25,058,877×
22,212,194×
22,128,811×
26,493,073×
25,900,034×
24,933,499×
24,429,454×
23,771,231×
20,787,907×
19,453,868×
23,835,792×
21,531,493×
18,831,945×
16,512,924×
20,542,872×
19,935,951×
23,356,551×
20,643,459×
17,400,839×
19,539,449×
17,703,887×
21,545,134×
24,174,778×
25,006,899×
22,457,500×
16,649,677×
13,707,228×
12,839,029×
12,834,231×
13,982,983×
14,693,113×
14,614,188×
16,581,501×
16,273,871×
13,617,520×
13,884,507×
13,799,374×
10,984,127×
13,094,187×
14,363,262×
13,060,337×
13,394,713×
13,570,632×
13,668,685×
17,817,019×
16,817,774×
15,708,731×
16,478,531×
16,970,176×
13,877,118×
20,890,381×
22,432,226×
17,874,957×
19,860,088×
22,236,816×
22,860,364×
21,363,359×
20,178,385×
16,775,171×
16,402,482×
17,177,798×
14,680,020×
17,462,027×
19,611,650×
19,769,102×
17,505,005×
16,502,127×
14,323,208×
15,453,651×
15,898,306×
19,740,169×
19,497,035×
16,946,211×
11,838,425×
13,762,168×
14,851,814×
16,498,402×
16,929,438×
15,819,768×
15,631,379×
18,686,714×
18,828,653×
19,195,648×
16,601,447×
16,647,313×
15,806,671×
15,856,030×
16,020,832×
17,332,141×
14,800,286×
15,448,133×
14,621,741×
12,706,011×
12,950,479×
11,477,079×
11,760,619×
13,669,727×
11,855,300×
10,865,533×
11,018,827×
11,042,397×
10,750,479×
10,329,651×
11,589,858×
11,626,477×
10,046,759×
7,432,279×
8,135,392×
8,776,729×
10,089,283×
10,372,450×
10,025,645×
7,955,743×
7,545,103×
7,727,750×
9,221,935×
8,585,362×
10,162,889×
8,687,437×
8,416,978×
10,054,977×
8,295,671×
8,814,674×
8,325,231×
6,898,441×
5,029,330×
4,765,846×
5,116,574×
4,272,561×
6,006,792×
5,500,090×
5,790,065×
7,556,130×
6,860,219×
5,175,220×
5,739,370×
6,369,179×
5,740,942×
5,711,085×
5,075,098×
3,025,523×
2,141,380×
2,830,690×
3,266,919×
3,665,133×
3,529,778×
3,890,521×
2,989,393×
3,519,331×
4,952,629×
5,733,537×
5,368,633×
4,497,974×
4,256,495×
4,789,167×
5,945,929×
4,303,526×
3,797,478×
4,296,926×
6,144,728×
5,274,238×
5,119,590×
6,173,622×
8,522,373×
9,085,319×
8,665,597×
8,951,508×
9,459,464×
8,070,475×
9,555,664×
9,517,422×
8,411,357×
6,818,372×
7,687,236×
10,146,800×
8,874,559×
9,802,554×
8,124,876×
8,114,599×
8,794,062×
11,536,131×
9,639,050×
10,280,863×
12,258,812×
13,855,297×
13,291,966×
12,958,004×
12,907,552×
14,776,895×
18,529,944×
15,016,839×
14,581,498×
14,422,890×
15,424,828×
20,232,963×
20,579,883×
19,831,758×
21,420,311×
21,986,881×
14,711,397×
14,064,256×
17,155,539×
24,004,445×
29,381,113×
32,536,746×
32,157,964×
21,650,829×
23,729,257×
31,404,758×
32,539,408×
36,030,811×
33,316,196×
24,885,986×
25,827,912×
27,800,932×
25,527,070×
28,025,732×
23,764,078×
26,879,593×
23,286,616×
25,164,259×
25,308,028×
26,552,371×
30,466,490×
27,051,897×
24,767,494×
24,371,454×
24,431,470×
25,535,109×
22,643,983×
22,902,816×
22,720,947×
21,732,069×
22,231,919×
24,002,673×
21,133,304×
17,576,822×
18,490,756×
16,278,004×
15,238,949×
15,605,245×
14,388,525×
14,741,769×
13,736,219×
14,193,497×
16,790,536×
17,132,731×
17,172,684×
18,407,927×
17,811,153×
19,534,523×
23,340,392×
21,947,142×
17,889,818×
16,389,483×
16,514,739×
17,871,008×
17,382,759×
17,093,182×
16,330,457×
18,831,674×
16,381,615×
17,024,959×
19,964,713×
21,214,216×
22,155,750×
19,442,675×
16,049,832×
19,311,568×
20,188,738×
16,535,493×
17,236,915×
16,495,929×
16,926,773×
15,168,680×
13,679,942×
16,498,897×
14,989,777×
15,315,144×
12,763,025×
13,114,008×
12,416,176×
13,383,780×
14,203,086×
10,636,948×
8,326,575×
7,824,753×
6,895,063×
5,944,318×
4,641,809×
5,796,508×
5,447,824×
6,761,787×
8,742,803×
8,688,013×
3,347,520×
2,828,974×
3,154,727×
2,697,220×
3,182,790×
2,487,483×
2,544,059×
2,999,015×
2,801,707×
2,902,922×
3,868,023×
2,785,248×
1,862,143×
1,695,344×
1,927,477×
2,494,516×
3,188,680×
4,031,544×
4,532,992×
6,840,283×
4,218,862×
3,455,462×
4,171,001×
5,113,097×
6,124,973×
5,056,925×
6,280,117×
8,111,013×
6,884,971×
7,100,237×
4,069,121×
3,891,798×
3,998,485×
4,635,120×
4,717,331×
4,158,096×
4,821,770×
4,790,026×
3,328,967×
3,343,192×
2,855,648×
3,178,630×
2,504,266×
2,561,153×
3,181,606×
3,635,941×
4,103,055×
3,673,265×
3,017,293×
2,986,287×
4,028,821×
2,093,549×
1,644,764×
1,140,484×
583,307×
346,446×
656,252×
741,764×
837,202×
442,904×
209,072×
288,403×
464,762×
441,856×
173,049×
41,076×
28,656×
54,294×
29,214×
24,116×
74,124×
19,992×
26,396×
101,192×
232,594×
424,848×
60,698×