Base 70: Iteration Frequencies: Cycle Start

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
Cycle Start		0.99 step
avg		1.47 step
avg		14.77 step
avg		2.93 step
avg		14.75 step
avg		69.74 step
avg		18.58 step
avg		224.76 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
69×
0s:
1s:
2s:
19×
1,276×
1,190×
0s:
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35s:
36s:
1×
1,329×
1,258×
2,514×
2,506×
2,494×
2,478×
2,458×
2,434×
2,406×
2,374×
2,338×
2,298×
2,254×
2,206×
2,154×
2,098×
2,038×
1,974×
1,906×
1,834×
1,758×
1,678×
1,594×
1,506×
1,414×
1,318×
1,218×
1,114×
1,006×
894×
778×
658×
534×
406×
274×
138×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
65,349×
175,984×
704,480×
70,864×
62,117×
5,823×
3,812×
0s:
1s:
2s:
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27s:
28s:
29s:
1×
100,049×
100,500×
85,498×
195,700×
248,294×
370,238×
401,896×
591,914×
619,452×
759,878×
894,816×
920,902×
1,076,996×
1,101,726×
1,211,064×
1,161,048×
1,182,282×
988,302×
1,051,110×
725,934×
761,030×
509,386×
438,688×
258,584×
183,676×
109,032×
45,920×
12,064×
2,784×
0s:
1s:
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277s:
1×
1,033,108×
2,830,029×
2,288,973×
2,694,746×
3,108,154×
3,422,351×
2,760,720×
2,686,991×
2,753,997×
2,349,020×
2,749,528×
2,811,094×
2,907,205×
2,667,740×
2,481,248×
2,741,378×
2,701,857×
2,509,288×
2,225,528×
2,593,474×
2,047,558×
1,933,565×
2,447,670×
2,179,038×
2,221,420×
2,514,494×
2,400,324×
2,446,953×
2,194,651×
2,430,002×
2,353,912×
2,319,534×
2,514,491×
1,998,333×
1,941,490×
2,108,919×
1,887,693×
1,695,863×
1,726,644×
1,751,358×
1,777,747×
2,044,936×
1,923,532×
1,676,072×
1,657,999×
1,448,360×
1,416,981×
1,291,783×
1,319,374×
1,147,372×
1,066,617×
1,005,788×
1,025,114×
835,273×
671,205×
655,628×
655,420×
778,676×
725,765×
799,461×
819,943×
932,094×
1,080,804×
1,118,382×
1,024,965×
918,131×
913,603×
925,804×
1,059,508×
939,639×
1,014,662×
676,522×
916,952×
747,160×
529,581×
473,536×
576,526×
856,186×
614,555×
621,544×
700,449×
660,390×
641,526×
685,316×
646,061×
787,870×
593,380×
643,160×
684,199×
757,670×
936,986×
776,335×
910,982×
983,259×
972,509×
924,849×
1,026,114×
1,047,714×
1,051,234×
928,946×
985,392×
952,308×
825,274×
773,155×
988,110×
1,317,807×
1,196,919×
1,285,789×
1,182,249×
1,071,292×
1,138,319×
874,528×
788,297×
764,089×
770,089×
764,229×
624,024×
581,171×
575,978×
404,157×
383,266×
274,394×
232,515×
308,888×
292,238×
169,938×
181,104×
209,586×
210,336×
234,627×
284,028×
205,225×
141,602×
166,693×
160,572×
184,476×
189,350×
92,617×
134,139×
65,175×
66,524×
113,905×
162,846×
134,959×
95,088×
130,067×
85,936×
95,621×
64,728×
44,112×
50,930×
77,388×
69,438×
92,346×
127,434×
116,304×
142,320×
66,113×
66,400×
47,287×
68,982×
62,586×
48,702×
31,256×
77,364×
133,455×
129,955×
194,716×
195,454×
184,740×
157,105×
111,827×
148,971×
149,578×
164,287×
150,636×
186,879×
239,082×
280,049×
190,158×
206,751×
215,646×
148,660×
115,607×
126,310×
162,985×
162,340×
204,632×
206,099×
148,682×
125,031×
182,904×
138,025×
187,715×
256,769×
194,650×
211,384×
241,064×
291,270×
259,784×
240,766×
252,610×
219,832×
333,610×
282,003×
173,353×
321,022×
176,852×
193,562×
223,095×
201,719×
295,196×
317,197×
395,876×
395,551×
357,219×
433,247×
319,158×
275,322×
231,135×
308,304×
228,419×
292,244×
159,396×
127,174×
74,075×
54,835×
97,649×
107,728×
68,194×
58,478×
69,858×
116,662×
95,192×
113,064×
84,126×
49,080×
97,661×
102,944×
220,149×
162,590×
253,113×
285,934×
265,338×
286,986×
294,104×
383,734×
338,047×
352,451×
454,598×
441,398×
377,134×
324,105×
325,145×
430,631×
464,811×
410,953×
499,082×
538,259×
420,361×
386,248×
281,347×
215,975×
205,466×
188,362×
214,851×
202,066×
249,526×
264,665×
199,857×
100,072×
97,351×
103,005×
31,992×
61,968×
39,668×
46,528×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
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27s:
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29s:
30s:
31s:
32s:
33s:
34s:
1×
438,459×
1,142,204×
3,005,366×
3,789,560×
5,950,262×
9,108,760×
13,791,056×
20,568,362×
30,111,256×
41,386,984×
54,438,526×
72,618,046×
88,409,000×
103,775,526×
111,929,030×
139,286,166×
161,277,066×
166,823,516×
176,218,514×
181,835,748×
162,568,348×
142,894,208×
137,023,782×
115,725,714×
85,865,424×
65,096,650×
45,654,142×
25,944,810×
11,769,658×
4,953,094×
1,775,712×
959,720×
39,922×
14,808×
0s:
1s:
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1×
11,474,243×
54,162,735×
46,552,159×
54,008,439×
54,232,821×
53,755,800×
56,792,251×
61,423,660×
61,493,677×
67,331,871×
72,038,531×
71,130,339×
76,646,249×
67,782,331×
69,827,174×
67,116,033×
70,328,356×
71,047,472×
69,934,030×
75,045,304×
73,023,137×
71,852,803×
73,856,541×
70,454,033×
70,913,842×
66,094,742×
68,888,524×
61,324,207×
51,309,052×
61,331,894×
65,980,324×
73,531,645×
73,852,790×
75,152,962×
77,436,630×
72,789,274×
76,318,505×
72,255,433×
67,614,871×
62,739,317×
63,620,642×
68,345,116×
76,458,006×
81,636,968×
84,261,881×
84,264,386×
80,670,213×
76,408,707×
69,009,979×
66,731,083×
68,841,322×
64,801,426×
69,447,320×
66,222,746×
68,268,838×
67,330,287×
64,517,341×
66,531,796×
62,175,947×
61,101,131×
65,138,259×
70,362,890×
65,602,848×
64,935,531×
65,462,927×
59,307,550×
60,153,638×
57,615,544×
55,054,923×
56,935,323×
50,695,704×
45,299,278×
46,006,224×
47,786,472×
47,062,303×
45,382,220×
44,570,814×
40,499,768×
37,242,463×
40,792,294×
44,259,211×
44,333,187×
48,603,982×
50,623,182×
54,439,423×
48,346,886×
47,863,225×
44,147,404×
48,145,304×
48,637,483×
50,828,228×
56,759,419×
48,581,305×
42,157,425×
43,088,572×
48,735,482×
55,020,263×
56,064,854×
53,772,183×
54,460,449×
58,715,197×
61,785,880×
54,382,472×
55,486,853×
58,784,979×
58,024,007×
61,063,954×
62,134,467×
62,712,974×
66,343,373×
67,113,881×
68,337,820×
61,884,975×
65,955,248×
66,319,528×
61,813,977×
63,742,670×
58,911,436×
58,556,683×
61,882,596×
67,744,895×
65,827,236×
65,682,253×
63,543,980×
62,287,331×
64,178,155×
65,212,500×
60,350,071×
57,644,259×
60,796,360×
61,482,164×
55,572,420×
58,430,373×
56,911,457×
57,877,513×
54,498,405×
49,127,528×
52,494,989×
56,968,306×
50,131,776×
49,944,516×
52,577,023×
62,996,773×
58,294,966×
61,471,819×
68,622,328×
64,105,829×
62,051,243×
60,611,482×
62,729,503×
59,639,320×
63,074,515×
60,685,328×
65,473,079×
61,018,238×
60,221,404×
62,326,651×
54,634,380×
52,091,706×
53,497,201×
55,288,881×
50,939,067×
50,214,970×
53,112,235×
55,797,599×
51,133,717×
48,405,764×
49,738,126×
53,908,996×
53,922,130×
51,855,953×
49,084,008×
45,319,613×
44,987,515×
40,718,435×
38,963,804×
35,505,558×
42,002,199×
41,474,360×
37,356,330×
38,914,540×
44,498,870×
48,811,592×
46,323,355×
50,224,094×
50,062,940×
47,993,026×
48,648,086×
50,945,182×
60,895,563×
57,391,980×
58,708,937×
58,916,131×
61,062,563×
61,216,029×
61,428,771×
60,840,399×
63,785,304×
58,675,781×
56,920,664×
61,050,127×
57,260,132×
56,556,653×
61,504,571×
65,358,517×
70,643,700×
77,164,051×
72,615,128×
73,818,028×
71,170,275×
73,423,729×
68,888,171×
68,754,301×
63,411,463×
60,914,898×
59,660,069×
62,688,013×
60,330,652×
53,540,083×
55,524,866×
60,449,852×
51,290,491×
48,341,802×
44,335,773×
41,065,029×
41,476,868×
40,626,616×
43,431,696×
38,280,148×
39,647,586×
43,519,236×
38,901,723×
38,920,534×
36,838,437×
35,800,358×
33,695,779×
32,106,932×
34,353,510×
38,713,914×
39,746,366×
38,996,604×
35,555,324×
36,245,105×
33,603,949×
36,327,127×
37,613,788×
36,675,820×
37,998,863×
36,094,554×
38,247,204×
35,719,989×
34,410,459×
33,717,357×
34,518,255×
35,248,257×
36,630,453×
34,263,879×
34,672,461×
32,962,438×
34,657,728×
30,818,577×
33,639,504×
31,589,548×
37,917,293×
35,556,703×
33,944,224×
34,842,488×
35,063,905×
32,525,146×
38,271,001×
38,015,348×
41,252,292×
38,118,030×
40,550,681×
32,647,260×
25,774,394×
26,207,738×
29,833,009×
32,662,543×
30,855,822×
34,052,910×
36,034,544×
31,942,144×
27,080,766×
26,608,766×
25,510,257×
27,122,705×
27,235,622×
28,224,698×
28,234,308×
29,307,249×
30,283,952×
29,617,141×
29,029,049×
33,278,449×
30,134,780×
29,765,291×
31,333,489×
33,632,939×
32,020,809×
30,751,235×
31,468,291×
34,396,938×
32,560,163×
29,764,005×
26,842,024×
25,074,600×
26,618,096×
25,701,412×
29,294,644×
26,779,227×
29,149,356×
25,937,183×
25,416,183×
31,636,680×
32,980,423×
31,911,318×
24,694,935×
21,988,007×
21,594,745×
25,647,088×
22,586,829×
19,296,475×
20,971,352×
21,355,715×
26,746,746×
22,317,121×
19,908,911×
13,454,232×
13,791,599×
16,913,843×
15,474,585×
14,285,746×
13,271,627×
12,757,761×
14,276,882×
12,304,586×
12,343,592×
14,601,671×
12,255,047×
11,688,795×
11,296,979×
13,423,382×
10,589,098×
9,789,594×
9,018,594×
9,206,490×
8,268,481×
8,427,996×
9,394,282×
9,201,451×
8,190,775×
9,629,153×
10,762,490×
11,261,182×
13,072,884×
14,713,650×
13,442,403×
11,712,155×
12,033,663×
13,025,911×
11,053,450×
12,153,043×
9,612,701×
8,373,243×
10,499,606×
12,292,202×
14,090,021×
13,821,432×
10,613,465×
11,059,987×
11,921,631×
12,611,308×
10,662,164×
9,156,669×
8,678,119×
11,451,746×
12,526,017×
11,863,543×
10,865,838×
11,734,551×
12,267,504×
12,144,820×
9,678,357×
10,433,517×
11,979,013×
11,255,053×
11,950,655×
11,696,217×
10,699,772×
11,687,009×
13,673,279×
10,520,847×
8,124,248×
6,170,846×
4,547,476×
4,114,769×
5,366,894×
4,503,433×
4,237,163×
5,218,517×
5,327,279×
3,458,242×
3,339,597×
2,371,588×
2,382,060×
2,802,816×
1,280,069×
1,505,336×
1,939,538×
1,628,888×
2,125,367×
2,254,542×
1,363,865×
1,210,488×
1,382,113×
1,727,100×
2,336,768×
2,071,646×
2,449,019×
3,085,895×
3,598,967×
3,371,787×
3,086,298×
3,034,534×
3,136,423×
4,466,177×
3,660,172×
2,303,710×
1,741,731×
2,436,012×
1,300,096×
825,933×
671,265×
589,782×
653,304×
698,324×
840,687×
1,186,148×
1,655,226×
1,213,081×
1,234,465×
1,802,973×
1,684,265×
1,781,468×
2,521,784×
2,464,962×
3,487,952×
4,245,399×
5,764,815×
8,280,257×
8,865,440×
6,410,732×
5,123,206×
4,872,728×
4,853,898×
3,517,132×
4,942,823×
3,413,047×
3,255,784×
2,537,010×
4,773,524×
5,736,509×
5,709,478×
8,062,916×
6,119,650×
5,983,964×
6,294,301×
4,431,366×
5,261,147×
6,520,829×
7,273,914×
7,065,140×
7,033,116×
5,095,207×
5,958,712×
4,446,380×
3,727,104×
4,346,498×
3,813,747×
4,107,991×
5,196,501×
6,005,294×
5,476,534×
7,047,150×
5,789,742×
5,008,624×
6,140,651×
6,689,989×
5,751,257×
9,180,252×
9,872,060×
11,015,587×
12,068,584×
10,410,637×
15,112,836×
13,659,447×
15,293,288×
15,840,513×
15,260,769×
19,997,951×
15,577,511×
18,201,658×
20,680,537×
20,370,437×
20,475,331×
18,555,882×
19,623,699×
19,613,711×
23,709,265×
27,193,335×
26,275,878×
28,600,559×
25,662,467×
19,794,783×
17,043,343×
18,798,342×
20,985,194×
19,345,365×
22,437,372×
28,553,611×
27,127,246×
26,017,450×
27,113,578×
25,340,163×
25,697,056×
24,132,781×
25,760,626×
29,972,082×
25,588,140×
23,239,760×
24,428,232×
26,539,631×
23,553,883×
23,509,152×
20,816,862×
22,103,252×
21,399,446×
19,554,116×
17,691,239×
19,953,538×
20,399,241×
20,053,804×
22,999,264×
29,082,194×
28,033,494×
26,795,520×
25,953,983×
24,030,561×
23,529,472×
21,823,494×
22,294,692×
21,301,823×
20,897,925×
19,667,654×
24,899,037×
25,535,833×
23,403,381×
20,435,168×
18,379,016×
18,496,877×
14,873,167×
17,129,014×
15,166,691×
15,383,947×
13,309,017×
12,292,560×
13,151,467×
13,630,815×
16,072,087×
16,589,012×
16,553,326×
15,693,429×
14,180,170×
12,679,299×
13,712,838×
13,952,551×
16,856,940×
18,627,925×
21,200,105×
21,772,441×
23,513,300×
23,797,137×
23,263,034×
25,266,029×
23,865,852×
22,688,259×
19,483,562×
19,304,475×
20,626,871×
25,920,452×
27,245,334×
23,319,478×
23,406,907×
20,148,709×
18,659,847×
20,545,484×
24,985,964×
24,245,339×
21,228,570×
21,062,658×
20,987,118×
20,270,534×
21,019,890×
21,862,263×
20,005,670×
24,748,256×
22,531,965×
20,992,263×
20,088,196×
19,290,127×
19,268,069×
16,065,247×
17,780,851×
15,863,158×
17,152,028×
18,121,897×
16,704,733×
15,537,356×
16,715,249×
16,962,078×
16,357,375×
15,830,747×
11,654,725×
10,055,377×
7,516,123×
8,908,405×
9,904,422×
12,417,034×
8,345,782×
6,872,306×
5,854,955×
8,263,456×
10,599,153×
11,621,405×
9,637,722×
8,228,889×
8,464,467×
8,042,124×
7,453,212×
5,626,032×
5,616,229×
6,274,457×
7,483,760×
6,567,692×
6,354,907×
5,777,173×
4,681,265×
4,162,029×
4,441,372×
4,820,612×
4,130,687×
4,096,830×
4,220,417×
4,271,682×
3,976,369×
2,970,662×
2,259,517×
2,941,947×
3,075,880×
3,503,816×
3,400,812×
2,013,850×
2,155,744×
2,358,227×
3,334,984×
2,753,313×
3,177,846×
1,983,865×
3,887,752×
5,386,657×
4,236,903×
4,895,997×
4,569,957×
4,475,904×
3,601,979×
3,730,444×
3,698,710×
3,017,666×
3,774,474×
2,797,687×
2,607,391×
3,101,426×
3,401,425×
4,727,281×
2,024,256×
1,485,488×
1,592,268×
1,412,503×
648,409×
314,166×
1,036,444×
2,020,920×
2,629,044×
2,774,657×
2,608,080×
2,912,380×
4,048,644×
4,006,030×
3,943,931×
4,866,205×
5,238,976×
3,927,000×
4,848,264×
5,734,163×
5,844,209×
5,792,423×
5,267,078×
6,994,838×
8,707,011×
5,566,285×
4,925,349×
4,390,865×
3,688,723×
4,728,979×
4,430,541×
5,832,163×
5,856,287×
6,227,154×
5,747,934×
5,474,745×
4,264,842×
4,443,155×
6,716,343×
6,681,077×
4,343,806×
4,314,147×
3,161,670×
2,453,680×
3,728,055×
3,494,887×
3,424,907×
5,539,727×
6,262,901×
3,755,834×
2,928,181×
3,005,584×
4,021,566×
4,465,700×
5,226,713×
5,426,658×
4,804,312×
5,351,295×
3,166,093×
2,154,120×
3,049,524×
4,353,326×
3,341,195×
2,599,726×
1,751,668×
1,832,531×
2,015,990×
1,998,016×
2,367,068×
1,602,237×
2,608,505×
1,797,557×
1,199,992×
1,216,340×
863,180×
793,380×
1,105,322×
718,319×
619,070×
643,807×
104,462×
171,350×
215,200×
371,492×
136,936×
151,490×
94,378×
161,256×
46,438×
82,752×
162,114×
139,893×