Base 58: 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		12.51 step
avg		2.98 step
avg		12.48 step
avg		55.62 step
avg		16.81 step
avg		228.52 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
57×
0s:
1s:
2s:
16×
883×
812×
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:
1×
927×
868×
1,734×
1,726×
1,714×
1,698×
1,678×
1,654×
1,626×
1,594×
1,558×
1,518×
1,474×
1,426×
1,374×
1,318×
1,258×
1,194×
1,126×
1,054×
978×
898×
814×
726×
634×
538×
438×
334×
226×
114×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
30,997×
81,718×
327,236×
40,157×
34,631×
4,041×
3,074×
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:
1×
58,195×
62,490×
50,778×
117,484×
147,458×
221,130×
251,892×
356,206×
408,534×
440,724×
495,386×
518,492×
562,062×
538,312×
550,140×
404,046×
438,532×
262,826×
246,644×
144,880×
103,230×
61,744×
24,086×
4,482×
1,248×
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:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
81s:
82s:
83s:
84s:
85s:
86s:
87s:
88s:
89s:
90s:
91s:
92s:
93s:
94s:
95s:
96s:
97s:
98s:
99s:
100s:
101s:
102s:
103s:
104s:
105s:
106s:
107s:
108s:
109s:
110s:
111s:
112s:
113s:
114s:
115s:
116s:
117s:
118s:
119s:
120s:
121s:
122s:
123s:
124s:
125s:
126s:
127s:
128s:
129s:
130s:
131s:
132s:
133s:
134s:
135s:
136s:
137s:
138s:
139s:
140s:
141s:
142s:
143s:
144s:
145s:
146s:
147s:
148s:
149s:
1×
280,011×
739,386×
780,371×
790,657×
769,413×
797,544×
725,632×
721,195×
816,000×
856,511×
816,562×
851,892×
741,453×
835,926×
777,218×
809,914×
866,241×
775,084×
923,142×
762,557×
660,539×
561,523×
710,736×
647,605×
629,503×
725,392×
674,075×
692,203×
764,880×
784,818×
916,238×
921,316×
965,653×
740,546×
652,043×
608,522×
657,898×
520,489×
482,956×
419,362×
516,118×
529,241×
535,940×
538,971×
497,533×
479,906×
463,142×
481,024×
394,854×
539,013×
489,438×
460,741×
449,622×
485,303×
572,997×
520,904×
584,647×
672,012×
629,536×
612,922×
559,335×
663,112×
626,089×
513,030×
499,025×
571,200×
557,983×
521,403×
570,395×
522,426×
589,580×
485,584×
419,655×
514,861×
454,774×
480,442×
370,614×
387,862×
325,161×
345,779×
390,275×
341,734×
298,714×
269,204×
347,142×
413,156×
436,461×
436,253×
329,405×
271,139×
293,941×
375,760×
416,030×
425,379×
374,043×
357,909×
331,648×
327,593×
350,097×
255,344×
313,385×
333,088×
395,533×
401,758×
348,736×
327,100×
304,209×
433,302×
447,009×
383,990×
377,736×
319,259×
298,537×
325,324×
270,834×
295,531×
291,320×
382,955×
414,098×
334,584×
298,118×
282,472×
354,795×
323,159×
250,226×
179,741×
228,088×
271,034×
208,380×
221,452×
157,036×
169,771×
106,328×
148,382×
165,080×
109,163×
71,459×
98,634×
83,282×
85,664×
77,642×
98,822×
79,134×
41,144×
25,230×
32,588×
43,496×
36,739×
53,766×
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:
1×
212,697×
564,152×
1,340,126×
1,705,340×
2,572,834×
4,225,270×
6,467,032×
8,820,440×
12,037,020×
17,405,038×
21,908,198×
27,176,168×
34,694,310×
41,546,710×
46,284,608×
50,732,496×
54,582,580×
50,391,050×
50,889,570×
51,643,610×
44,650,390×
35,598,272×
24,413,112×
17,529,350×
8,688,274×
3,350,910×
1,227,304×
438,990×
99,990×
20,236×
114×
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:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
81s:
82s:
83s:
84s:
85s:
86s:
87s:
88s:
89s:
90s:
91s:
92s:
93s:
94s:
95s:
96s:
97s:
98s:
99s:
100s:
101s:
102s:
103s:
104s:
105s:
106s:
107s:
108s:
109s:
110s:
111s:
112s:
113s:
114s:
115s:
116s:
117s:
118s:
119s:
120s:
121s:
122s:
123s:
124s:
125s:
126s:
127s:
128s:
129s:
130s:
131s:
132s:
133s:
134s:
135s:
136s:
137s:
138s:
139s:
140s:
141s:
142s:
143s:
144s:
145s:
146s:
147s:
148s:
149s:
150s:
151s:
152s:
153s:
154s:
155s:
156s:
157s:
158s:
159s:
160s:
161s:
162s:
163s:
164s:
165s:
166s:
167s:
168s:
169s:
170s:
171s:
172s:
173s:
174s:
175s:
176s:
177s:
178s:
179s:
180s:
181s:
182s:
183s:
184s:
185s:
186s:
187s:
188s:
189s:
190s:
191s:
192s:
193s:
194s:
195s:
196s:
197s:
198s:
199s:
200s:
201s:
202s:
203s:
204s:
205s:
206s:
207s:
208s:
209s:
210s:
211s:
212s:
213s:
214s:
215s:
216s:
217s:
218s:
219s:
220s:
221s:
222s:
223s:
224s:
225s:
226s:
227s:
228s:
229s:
230s:
231s:
232s:
233s:
234s:
235s:
236s:
237s:
238s:
239s:
240s:
241s:
242s:
243s:
244s:
245s:
246s:
247s:
248s:
249s:
250s:
251s:
252s:
253s:
254s:
255s:
256s:
257s:
258s:
259s:
260s:
261s:
262s:
263s:
264s:
265s:
266s:
267s:
268s:
269s:
270s:
271s:
272s:
273s:
274s:
275s:
276s:
277s:
278s:
279s:
280s:
281s:
282s:
283s:
284s:
285s:
286s:
287s:
288s:
289s:
290s:
291s:
292s:
293s:
294s:
295s:
296s:
297s:
298s:
299s:
300s:
301s:
302s:
303s:
304s:
305s:
306s:
307s:
308s:
309s:
310s:
311s:
312s:
313s:
314s:
315s:
316s:
317s:
318s:
319s:
320s:
321s:
322s:
323s:
324s:
325s:
326s:
327s:
328s:
329s:
330s:
331s:
332s:
333s:
334s:
335s:
336s:
337s:
338s:
339s:
340s:
341s:
342s:
343s:
344s:
345s:
346s:
347s:
348s:
349s:
350s:
351s:
352s:
353s:
354s:
355s:
356s:
357s:
358s:
359s:
360s:
361s:
362s:
363s:
364s:
365s:
366s:
367s:
368s:
369s:
370s:
371s:
372s:
373s:
374s:
375s:
376s:
377s:
378s:
379s:
380s:
381s:
382s:
383s:
384s:
385s:
386s:
387s:
388s:
389s:
390s:
391s:
392s:
393s:
394s:
395s:
396s:
397s:
398s:
399s:
400s:
401s:
402s:
403s:
404s:
405s:
406s:
407s:
408s:
409s:
410s:
411s:
412s:
413s:
414s:
415s:
416s:
417s:
418s:
419s:
420s:
421s:
422s:
423s:
424s:
425s:
426s:
427s:
428s:
429s:
430s:
431s:
432s:
433s:
434s:
435s:
436s:
437s:
438s:
439s:
440s:
441s:
442s:
443s:
444s:
445s:
446s:
447s:
448s:
449s:
450s:
451s:
452s:
453s:
454s:
455s:
456s:
457s:
458s:
459s:
460s:
461s:
462s:
463s:
464s:
465s:
466s:
467s:
468s:
469s:
470s:
471s:
472s:
473s:
474s:
475s:
476s:
477s:
478s:
479s:
480s:
481s:
482s:
483s:
484s:
485s:
486s:
487s:
488s:
489s:
490s:
491s:
492s:
493s:
494s:
495s:
496s:
497s:
498s:
499s:
500s:
501s:
502s:
503s:
504s:
505s:
506s:
507s:
508s:
509s:
510s:
511s:
512s:
513s:
514s:
515s:
516s:
517s:
518s:
519s:
520s:
521s:
1×
3,114,504×
15,507,816×
16,120,599×
18,710,572×
19,298,994×
20,098,302×
17,097,272×
17,252,370×
18,616,666×
19,182,432×
19,344,180×
18,415,490×
17,545,424×
17,403,629×
18,473,484×
18,689,607×
18,233,721×
18,815,955×
17,301,707×
17,862,387×
18,103,673×
17,547,596×
16,748,053×
14,419,449×
12,671,240×
12,233,387×
12,277,977×
12,024,994×
10,945,097×
11,823,543×
12,055,995×
14,114,486×
13,843,627×
15,163,092×
12,524,504×
11,421,572×
11,394,471×
12,302,512×
11,877,774×
12,372,331×
11,885,865×
13,262,288×
12,960,331×
14,225,970×
14,555,276×
14,218,418×
13,345,953×
12,683,495×
10,984,900×
10,581,772×
9,281,188×
8,479,052×
7,840,141×
6,110,792×
7,265,377×
7,252,030×
6,885,725×
6,401,276×
6,398,918×
6,314,171×
5,195,984×
4,723,657×
4,014,513×
5,614,726×
5,667,757×
5,371,209×
4,595,523×
4,352,207×
4,331,073×
4,526,495×
4,225,348×
3,717,088×
3,103,120×
3,937,096×
5,550,458×
6,899,566×
6,250,433×
6,584,204×
6,331,300×
6,850,251×
8,541,225×
9,136,177×
9,567,726×
8,967,430×
9,494,296×
9,369,807×
9,293,656×
6,628,352×
7,249,106×
8,046,479×
8,411,497×
9,186,711×
8,050,084×
7,283,194×
7,581,015×
8,261,069×
6,977,630×
6,516,536×
6,516,086×
5,882,052×
6,976,931×
8,593,497×
9,832,821×
9,238,258×
7,398,679×
6,057,264×
5,391,166×
5,006,393×
3,710,261×
4,102,383×
3,682,252×
3,546,003×
2,789,935×
2,494,771×
2,215,391×
2,791,162×
3,759,856×
3,329,971×
3,621,736×
4,024,537×
3,033,073×
2,892,509×
4,549,200×
4,906,135×
5,563,503×
6,032,609×
5,797,629×
5,993,727×
7,439,777×
9,414,752×
11,334,083×
11,855,887×
11,969,333×
10,521,388×
9,933,315×
10,787,113×
9,644,628×
10,537,558×
10,452,640×
11,418,597×
12,620,402×
10,778,357×
10,703,086×
10,656,448×
11,146,017×
12,018,109×
12,954,875×
12,067,959×
10,940,585×
12,071,152×
11,980,410×
12,208,218×
9,721,768×
10,156,584×
10,336,128×
10,281,349×
10,844,499×
9,666,878×
11,878,685×
12,758,189×
12,267,819×
9,754,097×
9,021,316×
9,496,285×
11,372,763×
11,169,583×
10,374,416×
11,310,056×
11,581,990×
12,277,275×
11,336,375×
12,030,964×
10,263,016×
8,601,141×
10,337,490×
9,675,696×
10,710,729×
11,045,592×
9,866,154×
9,769,184×
11,141,906×
11,028,618×
9,201,819×
7,909,015×
7,654,741×
7,494,019×
9,793,186×
10,106,439×
9,330,723×
8,679,595×
8,943,543×
10,856,365×
10,246,123×
11,026,870×
11,130,641×
10,378,217×
12,037,789×
12,283,840×
13,857,223×
12,361,962×
11,408,137×
11,857,674×
11,420,043×
10,585,735×
12,233,103×
14,725,409×
13,485,437×
12,470,805×
11,371,544×
11,465,444×
12,267,292×
11,181,276×
11,542,174×
11,286,485×
11,558,296×
11,391,115×
11,621,541×
11,113,814×
9,764,794×
9,169,831×
10,020,024×
11,105,805×
12,068,366×
11,905,052×
14,327,485×
14,942,893×
17,898,992×
18,628,868×
16,128,662×
16,824,739×
18,155,336×
20,344,753×
19,442,903×
20,096,173×
19,676,946×
19,585,188×
22,237,766×
21,150,990×
22,404,296×
23,154,706×
24,722,561×
21,603,622×
19,080,613×
18,806,732×
18,306,261×
18,202,380×
18,822,495×
18,894,423×
19,117,539×
19,354,858×
18,270,105×
16,697,610×
15,043,784×
13,383,065×
12,796,118×
13,151,161×
13,781,130×
13,980,763×
12,233,232×
13,447,043×
12,682,707×
14,197,484×
13,243,327×
12,339,209×
10,506,765×
11,019,053×
9,171,865×
10,732,541×
9,611,966×
10,316,365×
10,272,516×
10,687,669×
12,330,811×
11,041,671×
11,694,405×
10,951,102×
9,405,863×
10,453,841×
9,767,364×
9,270,437×
11,927,606×
12,903,779×
12,780,182×
12,212,698×
11,383,391×
13,032,565×
11,475,199×
10,877,303×
10,837,390×
12,065,697×
13,594,125×
13,485,928×
11,182,643×
12,577,532×
12,445,374×
13,704,686×
12,562,173×
11,470,309×
10,204,790×
10,253,495×
10,784,277×
10,604,784×
13,205,121×
13,006,816×
12,847,091×
13,644,136×
11,874,446×
13,754,207×
12,699,308×
12,633,446×
12,276,391×
13,873,049×
12,738,468×
13,652,286×
13,747,641×
14,666,658×
15,083,538×
16,034,717×
17,439,610×
15,447,803×
13,983,013×
14,488,638×
14,384,099×
17,194,585×
13,805,204×
12,322,639×
14,794,494×
16,841,806×
18,297,640×
14,393,516×
16,531,571×
20,168,221×
18,603,142×
15,071,151×
14,660,785×
15,788,476×
14,281,696×
14,443,531×
14,330,073×
14,486,833×
13,173,976×
12,986,114×
12,379,202×
13,714,858×
14,192,645×
14,004,309×
14,023,051×
13,260,662×
14,379,292×
14,272,330×
14,668,393×
14,199,047×
13,732,880×
12,445,712×
12,066,630×
12,159,272×
13,521,104×
12,673,891×
13,161,303×
13,510,816×
11,812,522×
12,659,122×
12,630,742×
13,535,099×
14,429,648×
12,737,923×
13,021,915×
12,975,029×
12,919,424×
12,136,520×
12,159,527×
10,452,853×
9,944,890×
10,677,591×
9,445,525×
9,231,754×
9,301,590×
8,443,196×
8,101,583×
8,504,337×
7,762,944×
6,942,137×
6,442,124×
6,725,137×
7,991,120×
8,765,704×
7,663,083×
8,636,127×
10,060,954×
9,011,081×
9,736,600×
8,748,334×
7,388,093×
7,914,990×
8,266,908×
8,255,018×
6,567,022×
6,800,382×
6,739,466×
6,317,882×
5,187,842×
4,052,268×
4,449,444×
4,635,290×
4,577,842×
5,098,377×
5,474,782×
5,527,833×
6,155,284×
5,454,437×
6,361,064×
7,410,446×
7,027,552×
7,981,532×
7,428,992×
6,485,855×
6,352,057×
5,385,272×
7,166,484×
5,808,608×
5,133,506×
5,678,027×
5,422,010×
5,651,866×
7,166,010×
6,829,115×
6,218,596×
6,590,063×
7,172,126×
7,908,358×
8,221,099×
7,667,086×
7,630,846×
7,282,926×
6,452,597×
5,818,068×
6,914,336×
6,180,102×
7,637,897×
6,707,139×
6,413,272×
7,812,362×
7,431,867×
6,064,603×
6,344,353×
6,508,797×
6,027,597×
6,975,933×
6,475,076×
5,335,043×
5,796,129×
6,403,633×
5,762,404×
4,715,722×
4,173,975×
4,206,405×
3,900,019×
3,898,810×
3,917,542×
3,997,546×
3,314,172×
3,135,131×
2,540,433×
2,394,195×
3,033,370×
2,387,413×
1,557,663×
1,351,005×
1,419,740×
1,114,744×
788,051×
1,143,878×
1,172,243×
1,113,953×
816,277×
1,075,589×
837,004×
1,118,636×
723,249×
564,243×
584,385×
736,492×
1,087,036×
1,148,576×
1,509,660×
2,040,486×
1,741,445×
1,846,570×
2,799,432×
2,933,347×
3,033,787×
2,670,801×
2,353,053×
2,584,716×
2,893,127×
2,364,344×
2,894,684×
2,461,041×
1,712,928×
1,506,277×
1,294,587×
843,460×
434,831×
536,888×
782,009×
330,833×
217,708×
179,633×
311,266×
702,160×
1,195,455×
1,488,354×
1,779,026×
1,079,748×
880,672×
719,355×
598,965×
723,366×
881,666×
410,049×
528,174×