Base 56: 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		1.46 step
avg		12.13 step
avg		7.01 step
avg		12.06 step
avg		41.73 step
avg		11.38 step
avg		145.62 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
55×
0s:
1s:
2s:
15×
825×
756×
0s:
1s:
2s:
3s:
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21s:
22s:
23s:
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26s:
27s:
28s:
29s:
1×
867×
810×
1,618×
1,610×
1,598×
1,582×
1,562×
1,538×
1,510×
1,478×
1,442×
1,402×
1,358×
1,310×
1,258×
1,202×
1,142×
1,078×
1,010×
938×
862×
782×
698×
610×
518×
422×
322×
218×
110×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
1×
2,349×
4,276×
14,640×
46,158×
164,238×
26,692×
20,788×
41,368×
73,342×
5,022×
5,536×
9,404×
17,872×
4,432×
2,104×
4,202×
11,540×
1,162×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
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15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
1×
31,237×
38,528×
45,962×
104,948×
143,080×
227,774×
249,910×
357,806×
379,414×
522,966×
457,072×
489,636×
404,186×
415,658×
362,394×
298,984×
267,736×
208,422×
157,850×
101,460×
76,682×
58,166×
39,628×
20,394×
1,618×
0s:
1s:
2s:
3s:
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5s:
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131s:
132s:
133s:
134s:
135s:
136s:
137s:
138s:
139s:
140s:
141s:
142s:
1×
357,214×
871,359×
788,802×
688,008×
786,423×
887,089×
870,916×
936,427×
864,451×
799,116×
889,480×
1,109,130×
1,158,579×
1,394,999×
1,464,223×
1,326,357×
1,160,315×
1,341,961×
1,261,969×
1,139,028×
1,014,996×
1,235,290×
1,004,656×
974,888×
1,050,318×
778,247×
771,967×
776,709×
712,042×
830,592×
698,637×
717,902×
836,710×
688,084×
630,524×
599,560×
592,384×
584,526×
587,522×
502,881×
462,970×
615,120×
624,727×
517,093×
391,345×
398,492×
419,208×
446,013×
472,277×
420,634×
477,247×
405,244×
240,274×
218,716×
138,294×
155,042×
74,087×
73,774×
102,568×
116,142×
162,164×
172,853×
245,216×
261,299×
234,118×
299,268×
355,903×
242,202×
142,821×
145,258×
153,911×
160,082×
177,967×
183,441×
206,906×
124,584×
137,910×
143,349×
139,028×
119,728×
131,736×
121,862×
168,426×
165,604×
103,842×
135,838×
148,813×
165,110×
122,158×
152,234×
171,058×
191,074×
151,389×
198,342×
205,404×
118,237×
97,112×
108,276×
68,512×
41,406×
64,028×
69,537×
74,958×
65,086×
71,584×
48,112×
69,152×
50,576×
86,952×
100,766×
99,416×
125,788×
174,082×
150,006×
195,634×
265,290×
336,119×
315,284×
394,724×
375,742×
426,285×
387,384×
271,560×
310,724×
231,948×
184,102×
151,816×
160,081×
146,354×
110,310×
90,968×
106,302×
172,490×
92,766×
84,708×
79,806×
67,954×
60,065×
82,528×
73,768×
36,845×
35,782×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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11s:
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13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
1×
929,403×
2,463,196×
5,343,774×
8,346,806×
13,547,318×
18,082,746×
24,875,528×
31,300,826×
39,695,944×
43,581,068×
49,383,876×
57,878,274×
53,198,380×
46,130,082×
38,966,772×
26,633,916×
17,049,656×
7,750,314×
3,762,782×
1,774,194×
815,318×
262,990×
17,136×
5,852×
0s:
1s:
2s:
3s:
4s:
5s:
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473s:
1×
2,332,558×
11,428,300×
11,701,905×
12,517,388×
18,356,575×
21,162,991×
19,405,293×
18,393,831×
19,701,905×
20,007,273×
18,453,075×
16,823,584×
18,247,484×
18,029,746×
19,800,575×
19,402,725×
18,951,969×
18,417,340×
17,391,076×
19,353,371×
19,211,443×
18,379,620×
17,624,570×
16,785,738×
15,959,053×
17,314,692×
17,005,073×
17,159,669×
16,881,096×
17,076,243×
16,587,094×
16,125,495×
13,900,411×
13,723,990×
13,793,628×
15,409,855×
18,011,110×
20,234,357×
21,605,896×
21,444,664×
20,231,840×
19,404,286×
19,126,828×
19,811,039×
19,511,770×
18,842,523×
17,774,755×
17,324,100×
16,854,140×
18,908,252×
18,605,383×
18,543,027×
16,940,920×
16,777,073×
18,994,799×
18,935,580×
16,809,378×
15,086,754×
15,455,978×
15,980,206×
16,535,266×
15,716,430×
17,270,995×
17,621,777×
18,833,692×
19,263,688×
17,069,218×
14,874,016×
16,428,380×
15,421,778×
14,860,852×
14,406,377×
14,735,027×
14,586,743×
14,516,232×
14,416,797×
14,617,127×
15,780,601×
16,564,819×
18,518,438×
18,280,614×
20,653,188×
21,783,613×
23,639,650×
21,741,686×
21,716,694×
20,826,151×
21,434,675×
22,059,040×
20,959,355×
18,869,226×
20,678,644×
20,674,303×
21,585,342×
23,281,135×
21,960,807×
20,787,153×
20,854,557×
21,836,297×
20,747,541×
19,701,667×
20,997,499×
19,073,000×
19,473,128×
20,174,936×
19,658,605×
18,375,093×
18,781,413×
18,645,074×
17,459,785×
15,990,924×
15,583,090×
14,839,822×
12,564,899×
14,407,044×
16,569,944×
15,676,436×
13,908,783×
12,837,114×
14,670,767×
14,138,206×
13,440,485×
11,579,476×
11,078,174×
11,457,081×
9,916,881×
10,099,649×
10,423,405×
9,287,846×
10,040,367×
9,108,057×
8,185,324×
10,012,825×
10,739,232×
10,853,316×
11,631,742×
10,273,919×
10,124,434×
8,829,909×
8,810,149×
7,830,206×
9,502,463×
9,567,913×
9,788,714×
8,190,389×
8,423,020×
8,693,257×
8,634,932×
8,695,742×
9,528,572×
10,246,328×
10,663,451×
11,596,773×
9,897,870×
7,916,120×
7,959,391×
7,849,442×
8,077,831×
8,663,253×
7,833,638×
8,311,773×
8,423,014×
9,961,186×
10,243,874×
10,256,469×
8,696,106×
8,117,988×
5,863,320×
5,372,152×
5,078,575×
6,045,053×
6,299,632×
5,353,415×
5,286,850×
5,818,082×
6,882,293×
6,351,244×
6,477,594×
7,905,084×
8,414,671×
8,237,114×
7,515,765×
8,240,828×
9,080,450×
8,916,192×
7,339,097×
6,988,548×
8,114,497×
8,575,999×
7,065,312×
6,064,684×
6,500,965×
6,149,657×
5,174,439×
5,427,743×
5,749,161×
5,539,871×
4,503,260×
4,011,089×
3,501,793×
2,888,991×
3,377,488×
3,080,614×
2,909,352×
2,615,270×
3,251,035×
3,301,411×
2,658,307×
2,401,988×
2,157,305×
2,590,427×
2,447,847×
2,699,580×
2,982,016×
2,832,697×
3,133,652×
3,515,239×
4,035,987×
3,914,777×
3,920,398×
3,315,359×
3,210,193×
4,586,650×
5,985,828×
7,214,571×
7,049,858×
7,482,979×
7,438,107×
7,623,609×
7,006,995×
7,337,308×
8,528,224×
9,040,365×
8,517,806×
7,625,134×
8,077,673×
8,786,519×
8,316,275×
8,633,277×
11,083,838×
9,599,927×
10,127,121×
10,741,221×
10,984,954×
12,677,537×
12,897,161×
11,672,265×
8,945,400×
7,715,287×
6,728,413×
5,631,320×
5,869,552×
5,394,793×
5,598,152×
5,133,451×
3,421,322×
2,924,753×
4,050,120×
5,061,372×
4,514,964×
3,249,109×
3,728,460×
3,871,544×
4,167,707×
4,453,016×
5,100,667×
6,476,959×
5,532,342×
3,791,507×
3,896,341×
4,459,899×
5,031,822×
4,306,001×
4,220,006×
4,356,227×
6,097,446×
6,011,855×
5,737,432×
5,075,032×
6,634,488×
6,057,535×
4,740,962×
4,438,337×
5,338,945×
6,489,241×
7,512,246×
6,700,863×
5,997,572×
6,125,579×
5,863,394×
4,598,936×
3,930,489×
5,341,055×
6,779,462×
6,725,663×
5,537,151×
6,613,107×
4,878,179×
4,819,654×
4,947,436×
6,336,946×
7,405,930×
6,140,205×
5,579,915×
4,786,167×
4,430,142×
5,501,196×
5,931,316×
6,004,474×
5,645,859×
5,880,652×
5,697,921×
5,326,202×
4,953,721×
4,649,354×
4,736,002×
5,628,290×
5,140,148×
4,486,453×
4,285,271×
4,486,388×
4,498,462×
4,023,807×
4,813,311×
6,041,924×
6,191,941×
5,051,337×
4,299,207×
4,919,576×
4,163,417×
3,477,518×
3,774,793×
4,137,040×
4,058,898×
3,579,020×
2,673,447×
3,368,384×
3,605,672×
3,583,706×
4,059,840×
3,228,023×
2,858,757×
1,936,326×
2,062,382×
1,949,688×
2,386,855×
2,804,093×
3,346,331×
2,522,397×
2,085,882×
1,826,401×
1,625,204×
1,448,513×
1,323,421×
1,355,571×
1,702,446×
2,296,828×
3,630,677×
3,078,451×
3,266,978×
4,227,395×
4,165,260×
3,842,330×
3,261,144×
3,275,147×
3,449,670×
2,698,282×
3,944,268×
3,754,387×
2,436,726×
2,856,975×
2,495,807×
1,923,805×
1,778,606×
2,377,413×
2,309,757×
1,309,017×
1,327,371×
1,589,016×
2,093,800×
2,574,073×
3,525,890×
3,270,850×
2,664,155×
3,341,404×
3,385,712×
4,798,472×
5,033,696×
5,005,147×
4,988,191×
5,354,060×
6,620,593×
6,474,556×
5,814,198×
5,487,165×
5,304,669×
5,082,462×
4,029,427×
3,920,624×
3,625,730×
4,111,627×
3,329,868×
2,924,192×
2,802,139×
3,213,389×
3,217,355×
2,946,921×
2,243,785×
2,321,754×
2,433,062×
2,929,346×
2,579,347×
2,581,434×
2,370,288×
2,299,904×
2,747,042×
4,000,371×
4,619,189×
4,070,372×
3,513,017×
3,830,716×
3,563,575×
2,944,434×
2,561,278×
2,939,857×
2,411,338×
2,209,176×
2,331,299×
1,601,120×
1,220,862×
1,115,536×
1,462,492×
1,156,218×
822,156×
567,350×
366,222×
334,847×
437,010×
508,250×
513,478×
707,759×
1,041,660×
1,219,062×
2,042,912×
1,278,531×
918,404×
541,070×
322,664×
314,158×
633,648×
1,033,632×
714,753×
494,304×
486,552×
784,738×
829,873×
571,099×
513,844×
1,318,695×
1,420,975×
1,595,214×
1,675,680×
1,532,768×
1,079,301×
1,107,973×
990,596×
1,099,872×
969,987×
524,066×
702,056×
251,136×
300,632×
48,580×