Base 69: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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		1.99 step
avg		11.08 step
avg		16.07 step
avg		22.32 step
avg		17.52 step
avg		134.70 step
avg		19.99 step
avg		218.29 step
avg
Step Frequency
Full Cycle
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1s:
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0×
1×
68×
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0×
1×
69×
117×
169×
223×
204×
0×
0×
0×
0×
0×
6×
390×
420×
816×
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0×
1×
68×
2,449×
1,221×
2,440×
2,430×
2,416×
2,398×
2,376×
2,350×
2,320×
2,286×
2,248×
2,206×
2,160×
2,110×
2,056×
1,998×
1,936×
1,870×
1,800×
1,726×
1,648×
1,566×
1,480×
1,390×
1,296×
1,198×
1,096×
990×
880×
766×
648×
526×
400×
270×
136×
0s:
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0×
1×
68×
0×
0×
0×
0×
0×
0×
0×
0×
0×
37,714×
100,705×
597×
0×
0×
0×
0×
0×
0×
0×
0×
210,996×
634,120×
43,365×
1,224×
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0×
1×
13,316×
19,301×
32,282×
70,922×
116,748×
203,976×
255,780×
378,356×
347,370×
642,032×
663,948×
908,179×
867,989×
1,097,500×
880,732×
1,144,422×
904,220×
1,070,078×
881,647×
891,462×
701,913×
716,993×
540,963×
488,931×
376,550×
310,440×
232,194×
149,188×
77,436×
29,075×
6,390×
0s:
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0×
1×
8,468×
13,900×
68,814×
47,191×
28,501×
17,423×
38,228×
27,469×
39,636×
37,128×
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×
143,089×
324,279×
657,784×
562,352×
614,211×
461,705×
659,385×
722,991×
658,420×
806,695×
912,670×
1,032,264×
857,322×
724,703×
731,202×
769,547×
727,500×
475,702×
488,182×
574,006×
619,614×
641,074×
859,047×
905,063×
889,889×
751,912×
624,546×
781,970×
836,363×
560,239×
621,594×
579,883×
543,974×
615,423×
398,718×
507,850×
500,216×
620,274×
509,258×
548,785×
348,547×
412,920×
387,744×
374,238×
504,265×
688,122×
757,557×
772,537×
718,364×
689,095×
794,517×
774,563×
812,392×
676,671×
760,517×
650,429×
567,521×
796,903×
868,174×
875,954×
925,932×
982,475×
808,459×
892,376×
706,589×
749,639×
714,011×
931,928×
1,042,445×
1,014,968×
996,431×
1,073,355×
1,102,234×
1,131,111×
1,468,336×
1,008,299×
1,120,195×
1,214,636×
1,252,356×
802,139×
733,886×
930,663×
952,988×
1,330,915×
1,327,540×
1,431,733×
1,820,868×
1,636,487×
1,866,906×
1,943,563×
1,997,484×
2,288,474×
2,569,480×
2,468,507×
2,042,156×
1,882,471×
1,910,650×
2,207,105×
2,217,388×
2,178,972×
2,123,971×
1,795,521×
1,565,709×
1,458,630×
1,323,385×
1,290,131×
1,575,702×
1,601,631×
1,539,711×
1,701,173×
1,482,511×
1,586,422×
1,658,246×
1,566,004×
1,625,116×
1,593,465×
1,700,525×
1,940,215×
1,829,083×
1,776,283×
1,590,972×
1,542,343×
1,259,959×
1,482,137×
1,597,038×
1,701,869×
1,440,264×
1,482,383×
1,417,653×
1,503,554×
1,640,206×
1,502,670×
1,627,360×
1,693,532×
1,581,262×
1,517,623×
1,556,619×
1,535,384×
1,077,075×
1,116,554×
1,170,066×
1,264,962×
1,097,488×
1,111,018×
801,524×
727,430×
892,498×
871,071×
961,103×
837,649×
972,749×
814,406×
638,977×
668,750×
730,818×
709,188×
797,758×
833,144×
1,055,937×
956,875×
993,311×
1,136,984×
920,707×
746,774×
701,795×
601,694×
608,378×
669,920×
506,846×
253,808×
181,126×
149,712×
260,989×
316,175×
175,316×
77,303×
110,334×
51,076×
144,844×
364,078×
166,483×
180,612×
24,464×
32,016×
27,010×
53,378×
46,815×
14,876×
21,138×
50,690×
51,441×
39,387×
4,364×
0s:
1s:
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35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
0×
1×
68×
415,412×
1,055,680×
3,311,212×
8,262,270×
15,215,696×
22,239,743×
29,351,848×
42,458,294×
51,729,663×
67,418,350×
83,080,227×
98,702,724×
106,703,410×
114,668,020×
125,041,727×
130,141,912×
120,726,985×
114,165,856×
108,309,305×
92,535,350×
81,066,512×
72,006,125×
65,341,986×
60,725,707×
60,870,220×
57,297,184×
56,772,219×
47,119,383×
41,098,651×
29,676,562×
24,737,905×
21,316,027×
15,579,800×
9,195,284×
3,572,125×
1,919,993×
776,498×
158,798×
62,672×
2,446×
0s:
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0×
1×
25,460×
209,868×
148,160×
195,136×
688,250×
3,666,326×
4,145,159×
3,878,235×
7,855,603×
14,453,149×
10,790,401×
17,015,710×
8,137,163×
9,637,408×
12,691,210×
17,541,908×
25,084,212×
20,518,920×
19,553,024×
12,074,258×
10,818,491×
10,760,455×
19,984,041×
30,177,640×
31,218,067×
26,980,492×
24,161,381×
22,075,669×
18,560,060×
21,152,000×
13,794,010×
15,305,348×
13,929,497×
21,482,871×
16,248,042×
6,656,562×
10,602,782×
7,388,325×
7,429,274×
8,001,934×
8,027,242×
12,939,261×
9,153,537×
5,470,499×
5,885,380×
9,608,900×
6,147,078×
7,012,500×
6,122,073×
10,110,160×
3,312,445×
3,739,795×
8,456,517×
5,405,468×
5,439,403×
5,870,305×
9,602,177×
12,983,432×
21,811,901×
26,798,161×
26,084,851×
31,005,556×
35,550,426×
42,633,149×
46,229,488×
54,318,298×
52,206,333×
52,589,370×
53,445,897×
48,869,806×
56,091,517×
47,068,457×
42,326,295×
52,378,014×
42,013,990×
46,707,713×
43,976,208×
42,768,853×
48,951,690×
59,042,587×
80,244,083×
79,172,703×
60,735,305×
73,515,694×
62,571,142×
64,218,655×
53,727,006×
55,311,253×
49,425,482×
49,047,847×
47,179,252×
50,759,323×
57,015,757×
57,959,044×
45,706,712×
56,219,566×
50,249,913×
58,781,266×
76,466,112×
74,167,029×
72,790,539×
69,520,929×
71,565,440×
74,130,146×
57,283,625×
53,724,218×
50,037,781×
50,784,720×
62,740,188×
67,028,813×
57,864,437×
73,714,806×
80,497,891×
74,312,886×
62,460,912×
58,497,374×
66,480,251×
70,944,868×
58,483,276×
71,382,431×
76,827,169×
68,098,301×
62,259,604×
54,665,482×
52,771,504×
64,852,848×
61,413,545×
60,396,618×
65,132,150×
79,835,760×
75,021,756×
71,797,869×
58,317,722×
48,176,366×
35,517,972×
37,568,474×
38,430,760×
38,636,108×
42,537,127×
41,858,688×
42,159,206×
49,150,557×
37,929,952×
40,476,951×
52,863,429×
74,301,031×
67,964,485×
67,464,666×
75,645,467×
78,476,144×
100,040,606×
104,787,492×
102,169,716×
84,968,096×
109,936,654×
90,603,953×
89,281,821×
74,490,976×
70,007,856×
82,065,651×
92,076,466×
87,784,003×
81,540,583×
91,655,392×
107,129,964×
98,237,409×
128,916,334×
109,381,610×
87,455,953×
79,412,192×
86,109,322×
99,228,391×
102,065,324×
101,630,390×
86,658,125×
90,839,011×
74,770,884×
71,229,055×
69,758,945×
69,644,661×
75,552,149×
72,765,323×
72,136,661×
68,918,654×
73,723,739×
70,402,683×
84,512,090×
98,973,376×
102,176,092×
99,357,494×
90,723,544×
97,957,084×
97,489,945×
112,177,787×
121,356,577×
100,368,749×
79,074,730×
69,120,819×
78,581,866×
82,312,423×
84,271,322×
79,585,767×
93,825,305×
75,647,837×
78,784,126×
79,357,190×
98,929,447×
75,408,085×
66,918,711×
77,965,141×
71,288,756×
74,661,901×
89,375,107×
62,755,034×
66,849,537×
70,681,866×
69,960,372×
74,254,618×
68,654,222×
45,216,080×
40,450,426×
39,877,217×
39,397,103×
43,051,871×
43,077,389×
28,633,165×
26,583,945×
26,619,325×
22,709,756×
20,200,200×
26,918,302×
19,845,021×
18,425,544×
20,088,278×
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24,239,926×
28,084,968×
33,542,963×
23,137,355×
20,383,745×
17,114,479×
17,888,258×
16,685,088×
18,158,980×
13,453,992×
14,724,229×
15,150,229×
15,895,941×
9,804,441×
13,130,526×
21,511,173×
19,795,244×
16,989,568×
12,156,520×
7,490,609×
11,570,876×
10,593,527×
9,634,557×
12,344,799×
10,190,114×
11,714,025×
8,595,888×
11,000,890×
19,892,853×
21,553,498×
13,140,611×
14,679,667×
14,878,259×
7,594,172×
8,306,725×
16,988,618×
19,913,679×
12,028,638×
18,295,611×
13,100,331×
18,313,888×
18,552,454×
25,383,293×
16,544,432×
11,849,834×
15,350,264×
11,716,667×
11,648,783×
6,221,549×
6,097,472×
3,582,650×
1,927,876×
2,946,197×
721,052×
1,435,340×
2,207,950×
3,118,178×
2,633,355×
801,980×
586,401×
797,578×
697,586×
1,265,862×
3,061,804×
6,650,274×
12,002,079×
8,428,528×
12,414,835×
9,151,979×
4,572,177×
4,676,125×
8,851,711×
5,550,358×
3,942,526×
3,131,085×
4,321,654×
5,531,516×
5,865,686×
7,034,202×
6,838,744×
6,751,089×
6,703,445×
6,557,624×
9,410,719×
23,864,943×
22,540,620×
26,843,536×
24,416,271×
19,961,438×
22,216,625×
21,914,378×
20,443,217×
21,322,831×
32,690,400×
36,941,344×
46,748,867×
58,549,898×
56,381,963×
58,185,184×
65,883,579×
61,434,374×
53,174,923×
60,558,864×
70,827,876×
94,504,562×
112,252,364×
94,426,654×
86,299,356×
94,121,081×
81,706,643×
101,154,708×
103,712,027×
83,477,068×
70,435,658×
72,317,088×
71,255,854×
83,723,649×
65,444,154×
67,825,486×
75,955,015×
84,901,877×
65,407,066×
67,868,171×
75,351,444×
59,926,683×
58,019,176×
54,311,162×
50,408,888×
43,144,178×
42,106,894×
44,423,444×
51,236,065×
61,178,744×
64,261,921×
63,094,799×
54,027,951×
51,710,915×
68,188,836×
68,411,083×
81,837,164×
67,146,721×
60,125,468×
74,468,785×
74,055,767×
84,347,146×
115,257,255×
99,029,024×
87,168,270×
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82,317,459×
68,840,434×
77,732,859×
74,446,947×
59,131,447×
66,394,222×
73,369,411×
72,042,383×
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59,510,533×
62,116,381×
55,122,007×
56,311,576×
44,538,584×
47,024,415×
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31,893,929×
27,376,529×
29,058,467×
27,837,644×
20,407,934×
14,153,160×
17,220,439×
14,651,749×
8,997,132×
6,445,186×
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10,100,453×
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10,782,325×
6,002,195×
13,123,369×
11,809,409×
13,772,613×
18,443,422×
19,190,814×
11,390,990×
7,186,741×
4,906,651×
1,789,584×
3,795,228×
7,317,512×
9,757,325×
6,816,656×
7,726,691×
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24,419,651×
19,103,050×
18,287,079×
21,097,284×
13,681,600×
5,625,143×
9,129,617×
7,352,702×
6,785,464×
3,318,540×
2,406,244×
1,716,023×
1,485,198×
1,869,887×
1,088,477×
495,940×
13,500×