Base 9: Iteration Frequencies: Full Cycle

Radix Character Encoding
0	1	2	3	4	5	6	7	8

Radix Character Encoding

Color Key
Orange	Fixed Point	number that becomes itself after one iteration
Green	Final Numbers	all numbers eventually reached, from all cycles
Purple	Cycle Start	iterations include entry into cycle, assuming it repeats
Red	Full Cycle	iterations include entire cycle, proving it repeats
Blue	Start Numbers	subset (optimization) of all numbers; minimal for full coverage
Gray	No Results	any calculation that has no results

Color Key

Orange

Fixed Point

number that becomes itself after one iteration

Green

Final Numbers

all numbers eventually reached, from all cycles

Purple

Cycle Start

iterations include entry into cycle, assuming it repeats

Red

Full Cycle

iterations include entire cycle, proving it repeats

Blue

Start Numbers

subset (optimization) of all numbers; minimal for full coverage

Gray

No Results

any calculation that has no results

Digits

Average Steps
Full Cycle

1.89 step
avg

3.60 step
avg

4.48 step
avg

5.15 step
avg

7.68 step
avg

17.39 step
avg

8.86 step
avg

14.91 step
avg

15.69 step
avg

11.68 step
avg

14.94 step
avg

10.35 step
avg

11.54 step
avg

20.54 step
avg

10.83 step
avg

13.79 step
avg

12.72 step
avg

25.16 step
avg

12.62 step
avg

24.89 step
avg

13.42 step
avg

31.72 step
avg

18.01 step
avg

21.62 step
avg

12.01 step
avg

25.92 step
avg

24.78 step
avg

44.20 step
avg

21.72 step
avg

30.55 step
avg

20.08 step
avg

40.85 step
avg

31.42 step
avg

47.36 step
avg

22.95 step
avg

27.38 step
avg

35.89 step
avg

27.23 step
avg

35.36 step
avg

24.93 step
avg

54.38 step
avg

27.12 step
avg

51.74 step
avg

29.81 step
avg

30.57 step
avg

35.86 step
avg

44.32 step
avg

29.62 step
avg

45.17 step
avg

42.28 step
avg

59.97 step
avg

40.65 step
avg

61.89 step
avg

25.91 step
avg

94.88 step
avg

28.67 step
avg

62.22 step
avg

47.45 step
avg

77.40 step
avg

32.81 step
avg

106.56 step
avg

40.54 step
avg

61.43 step
avg

54.19 step
avg

51.14 step
avg

59.14 step
avg

45.68 step
avg

34.38 step
avg

59.05 step
avg

43.67 step
avg

69.32 step
avg

65.75 step
avg

61.62 step
avg

31.59 step
avg

95.82 step
avg

56.81 step
avg

69.42 step
avg

37.73 step
avg

Step Frequency
Full Cycle

0s:
1s:
2s:
0×
1×
8×

0s:
1s:
2s:
3s:
4s:
5s:
0×
1×
9×
13×
6×
16×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
0×
1×
8×
49×
21×
40×
30×
16×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
0×
1×
8×
0×
80×
250×
132×
24×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
0×
1×
56×
45×
0×
0×
190×
295×
254×
197×
136×
89×
24×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
0×
1×
8×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
329×
911×
789×
250×
118×
168×
272×
157×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
0×
1×
8×
112×
180×
276×
580×
594×
809×
907×
1,144×
1,214×
450×
160×

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:
0×
1×
80×
128×
0×
216×
570×
878×
590×
543×
754×
907×
413×
357×
210×
285×
1,147×
1,038×
714×
831×
771×
370×
398×
636×
548×
357×
18×
32×
68×
10×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
0×
1×
116×
132×
400×
590×
746×
306×
362×
345×
24×
0×
0×
945×
1,846×
3,253×
3,353×
2,903×
2,397×
3,030×
2,343×
967×
161×
90×

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:
0×
1×
56×
72×
245×
337×
1,614×
4,778×
6,427×
4,457×
2,666×
2,921×
2,945×
1,757×
1,668×
3,583×
3,777×
1,970×
2,157×
1,106×
540×
287×
186×
123×
53×
32×

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:
0×
1×
80×
144×
0×
0×
0×
708×
2,404×
3,702×
4,999×
6,860×
5,705×
4,981×
4,888×
6,281×
6,580×
8,159×
5,638×
3,711×
3,485×
2,212×
1,765×
1,373×
943×
389×
426×
148×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
0×
1×
8×
289×
1,697×
6,325×
9,043×
13,688×
12,507×
13,251×
7,924×
15,084×
12,513×
10,693×
5,409×
7,021×
3,884×
2,908×
3,120×
377×
228×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
0×
1×
80×
120×
0×
540×
2,924×
9,240×
19,971×
25,080×
26,027×
25,964×
26,769×
16,880×
12,434×
11,691×
11,598×
5,888×
4,008×
3,234×
426×
599×
16×

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:
0×
1×
224×
900×
2,884×
296×
312×
0×
0×
0×
0×
0×
790×
4,641×
17,492×
15,955×
19,865×
24,010×
29,898×
35,049×
22,939×
21,676×
32,236×
17,582×
11,420×
13,371×
12,149×
6,116×
3,087×
2,438×
4,398×
7,035×
3,831×
2,594×
1,364×
2,510×
1,916×
227×
165×
191×
123×
53×
32×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
0×
1×
56×
144×
568×
2,656×
10,426×
27,781×
64,054×
69,181×
70,603×
75,820×
53,630×
42,779×
20,753×
11,578×
12,437×
14,719×
5,638×
3,612×
1,617×
1,662×
519×
80×

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:
0×
1×
80×
309×
1,589×
6,459×
17,234×
20,816×
41,220×
52,345×
65,134×
45,660×
56,633×
51,815×
64,484×
40,679×
50,977×
66,833×
40,950×
28,169×
24,256×
28,318×
11,053×
13,358×
3,893×
2,420×
456×
245×
53×
32×

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:
0×
1×
336×
3,992×
13,544×
36,601×
37,676×
38,246×
38,310×
35,456×
61,031×
113,387×
107,819×
116,595×
149,930×
102,866×
72,254×
55,087×
33,440×
19,629×
10,763×
7,107×
9,221×
5,140×
5,482×
5,045×
1,445×
1,172×

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:
0×
1×
188×
1,164×
1,992×
3,916×
6,853×
4,070×
3,864×
7,750×
50,910×
49,470×
80,105×
80,940×
72,931×
55,831×
105,736×
88,426×
83,061×
71,787×
64,357×
41,074×
36,822×
20,780×
13,862×
15,437×
13,975×
47,668×
26,168×
14,312×
6,825×
19,153×
47,407×
38,822×
23,997×
32,967×
19,626×
27,691×
26,267×
14,905×
5,728×
3,541×
3,951×
2,856×
4,476×
3,108×
4,726×
3,516×
7,953×
12,207×
20,831×
39,792×
38,799×
40,996×
27,824×
10,207×
5,341×
3,034×
1,584×
214×
445×
36×

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:
0×
1×
480×
4,268×
10,508×
9,296×
29,980×
79,365×
191,867×
197,032×
219,893×
242,175×
226,299×
180,269×
167,807×
141,756×
140,965×
122,539×
72,617×
52,126×
40,206×
32,393×
25,128×
14,461×
10,579×
3,906×
2,645×
801×
544×
100×
44×
25×

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:
0×
1×
128×
576×
472×
16×
0×
377×
2,616×
10,773×
3,952×
3,520×
1,132×
308×
0×
0×
1,515×
30,773×
149,313×
254,859×
214,273×
267,851×
179,708×
221,173×
262,654×
231,481×
274,980×
194,624×
129,287×
106,379×
85,122×
97,046×
99,153×
92,061×
50,065×
44,830×
12,855×
6,088×
9,309×
23,168×
9,897×
9,698×
11,086×
11,067×
3,651×
268×

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:
0×
1×
336×
2,708×
5,704×
7,476×
26,020×
58,556×
84,961×
160,299×
350,411×
568,684×
585,984×
528,937×
507,937×
415,364×
320,550×
233,640×
135,830×
102,092×
57,946×
38,269×
21,254×
32,181×
12,775×
14,889×
13,393×
5,560×
317×
55×
16×

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:
0×
1×
80×
1,064×
10,944×
24,488×
25,431×
90,157×
30,047×
4,556×
0×
945×
16,999×
72,176×
55,007×
88,661×
65,299×
110,424×
177,701×
125,230×
89,109×
76,689×
127,598×
164,390×
143,575×
77,144×
108,971×
148,076×
243,942×
409,322×
330,507×
405,855×
256,642×
251,313×
174,814×
135,878×
109,539×
84,441×
47,991×
81,222×
191,812×
191,472×
77,720×
75,362×
65,662×
121,739×
76,273×
57,980×
44,508×
38,328×
33,358×
86,557×
76,989×
60,630×
76,782×
45,748×
75,067×
53,656×
23,836×
6,638×
3,109×
2,335×
1,136×

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:
0×
1×
552×
5,480×
18,860×
58,264×
133,172×
208,793×
162,529×
165,595×
209,416×
286,551×
505,037×
575,060×
590,247×
429,603×
403,924×
336,896×
275,804×
297,214×
298,719×
309,798×
326,692×
334,311×
308,558×
401,617×
334,792×
265,299×
145,418×
108,233×
100,402×
92,523×
114,519×
34,689×
27,853×
12,846×
6,150×
2,687×
621×

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:
0×
1×
224×
3,296×
14,346×
12,650×
77,745×
124,690×
169,962×
226,366×
265,986×
255,878×
291,976×
313,978×
434,421×
467,687×
405,333×
437,172×
553,025×
650,875×
734,519×
454,829×
411,118×
431,023×
251,727×
230,019×
277,270×
180,330×
328,520×
354,722×
387,066×
281,597×
188,847×
180,687×
221,277×
148,708×
172,387×
197,585×
158,905×
78,580×
73,053×
33,829×
21,796×
10,836×
2,825×
507×
35×
92×

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:
0×
1×
384×
4,036×
37,112×
144,080×
490,532×
884,400×
913,439×
1,163,851×
1,672,525×
1,623,117×
1,403,557×
1,401,150×
1,117,829×
844,181×
511,103×
443,277×
336,628×
249,619×
168,411×
96,691×
119,032×
75,104×
36,918×
41,758×
61,485×
27,216×
12,094×
2,231×
2,147×
176×
72×

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0×
1×
444×
6,308×
44,384×
126,668×
288,636×
413,013×
668,702×
991,937×
892,474×
834,479×
628,856×
494,653×
365,539×
217,044×
163,147×
114,538×
89,631×
54,350×
24,549×
15,534×
169,265×
787,144×
2,015,848×
1,679,226×
1,541,403×
1,590,080×
1,251,854×
945,886×
783,958×
710,630×
697,528×
479,229×
687,494×
535,410×
560,669×
377,759×
306,516×
231,598×
215,294×
163,155×
137,059×
175,090×
341,811×
324,946×
131,199×
114,742×
78,107×
47,160×
9,697×
7,821×
2,420×
537×
398×

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0×
1×
128×
840×
736×
0×
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0×
2,075×
111,683×
752,779×
2,256,322×
1,853,062×
1,900,085×
1,986,183×
1,791,891×
1,586,235×
1,663,695×
1,531,625×
1,169,552×
615,980×
455,158×
329,635×
288,098×
298,088×
802,340×
1,704,765×
1,488,185×
1,410,355×
1,664,993×
1,319,682×
899,179×
1,215,075×
1,189,222×
1,219,594×
1,199,033×
766,410×
871,020×
620,140×
1,050,612×
607,282×
586,219×
574,588×
724,876×
468,995×
596,388×
558,795×
461,516×
505,157×
362,595×
358,160×
668,884×
709,691×
489,958×
293,697×
390,504×
468,620×
738,046×
355,697×
506,703×
602,687×
414,505×
339,578×
170,460×
190,153×
216,291×
151,103×
132,440×
38,350×
67,816×
49,889×
43,194×
22,831×
9,597×
3,745×
4,357×
4,640×
841×
55×
95×
29×
9×

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0×
1×
408×
4,300×
35,932×
131,616×
368,932×
591,776×
973,616×
1,835,954×
2,034,850×
2,805,590×
3,496,665×
3,041,214×
3,243,913×
2,763,492×
2,666,221×
2,221,814×
2,480,178×
3,020,357×
3,248,696×
2,473,091×
2,021,848×
2,455,845×
2,641,759×
2,184,891×
1,382,986×
1,092,334×
1,354,840×
1,805,864×
1,005,428×
814,797×
1,383,809×
1,474,828×
1,172,243×
933,725×
731,504×
496,252×
273,531×
324,503×
311,132×
108,785×
55,332×
36,679×
19,656×
2,536×
25×

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0×
1×
552×
9,160×
36,476×
108,104×
260,920×
642,488×
1,986,994×
4,090,662×
2,985,387×
3,287,295×
2,428,840×
2,114,418×
1,857,883×
1,697,586×
1,474,542×
1,238,875×
1,038,334×
1,218,915×
924,977×
606,229×
355,630×
301,649×
393,059×
340,645×
266,319×
350,300×
501,541×
510,181×
211,621×
571,900×
2,722,385×
5,921,117×
4,956,885×
5,149,056×
5,148,882×
4,227,966×
3,268,967×
2,675,509×
2,945,909×
2,190,531×
2,257,957×
2,471,384×
2,785,922×
3,114,088×
2,859,373×
2,699,224×
2,307,081×
1,923,636×
1,358,238×
989,015×
654,506×
479,916×
360,553×
102,533×
108,319×
41,417×
14,433×
1,884×
76×

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0×
1×
516×
37,052×
146,052×
290,460×
344,172×
1,438,204×
3,594,776×
1,747,834×
2,456,978×
2,275,842×
2,593,837×
5,061,622×
3,186,052×
3,400,936×
5,259,752×
5,199,959×
4,626,517×
5,678,435×
6,528,195×
6,512,070×
6,667,976×
7,275,565×
7,218,197×
5,459,095×
6,261,971×
5,129,377×
4,455,170×
6,085,685×
6,041,583×
5,621,555×
4,370,122×
3,505,724×
3,529,802×
4,376,517×
3,198,621×
2,868,889×
3,983,385×
3,210,065×
2,557,535×
2,196,032×
2,061,494×
2,187,178×
1,199,667×
1,141,126×
1,994,920×
1,770,572×
1,668,264×
1,217,046×
1,212,538×
629,767×
1,291,200×
815,950×
1,355,027×
962,770×
1,186,354×
622,901×
1,028,613×
309,073×
103,592×
58,267×
21,838×
821×
655×
662×
204×

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0×
1×
552×
10,304×
42,172×
125,228×
406,128×
2,147,188×
6,951,598×
4,895,663×
5,546,815×
5,734,838×
4,490,876×
3,404,781×
2,933,688×
3,506,288×
3,841,972×
3,908,915×
2,727,094×
2,334,581×
2,082,158×
3,016,689×
5,397,548×
4,639,299×
4,370,272×
4,173,848×
4,711,321×
3,609,668×
4,673,830×
4,827,990×
3,549,000×
2,484,219×
3,302,571×
3,685,554×
3,364,658×
3,487,808×
3,052,902×
2,540,701×
2,262,102×
2,452,427×
2,339,480×
3,462,168×
3,696,910×
2,564,201×
2,595,533×
2,470,096×
2,305,376×
3,170,584×
2,606,833×
2,393,981×
2,673,934×
3,367,249×
3,849,574×
3,313,141×
2,460,948×
2,349,782×
2,957,209×
2,605,206×
2,020,049×
2,074,721×
3,812,933×
5,077,547×
3,868,676×
3,901,577×
3,432,331×
3,097,041×
2,154,607×
1,499,491×
2,365,081×
1,585,015×
872,953×
1,191,944×
997,618×
776,229×
585,495×
232,527×
86,095×
38,538×
6,054×
1,196×
25×

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0×
1×
624×
40,208×
124,948×
258,180×
299,564×
948,184×
1,311,453×
891,951×
2,904,607×
7,808,559×
9,125,746×
7,532,928×
6,294,822×
4,870,221×
9,232,297×
11,644,313×
11,972,251×
11,691,438×
7,833,425×
6,786,641×
7,490,647×
6,617,439×
8,085,864×
10,683,936×
11,190,881×
9,510,619×
7,679,162×
5,794,646×
4,782,745×
4,705,093×
4,595,235×
4,356,753×
3,170,060×
3,467,711×
3,810,908×
3,748,204×
4,095,712×
4,862,773×
3,881,457×
4,420,519×
4,532,496×
3,755,556×
3,765,906×
2,451,815×
2,778,731×
3,063,569×
3,249,757×
3,546,074×
4,232,198×
3,548,215×
2,225,522×
989,072×
523,816×
838,433×
1,246,186×
546,443×
273,394×
128,749×
99,418×
206,757×
157,828×
33,848×
151,351×
50,588×
11,885×
1,720×
699×
64×

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0×
1×
552×
12,532×
78,484×
122,072×
436,464×
2,169,648×
6,256,866×
5,558,589×
7,140,438×
7,092,294×
5,816,644×
4,555,043×
5,107,891×
5,170,503×
4,672,995×
4,595,105×
5,764,884×
9,009,048×
6,400,746×
8,173,443×
10,572,887×
7,883,222×
6,977,888×
5,834,795×
5,407,836×
3,263,655×
3,421,852×
4,071,931×
3,389,587×
2,324,750×
2,680,706×
3,038,202×
3,471,874×
2,964,913×
3,588,783×
3,806,436×
5,383,090×
5,800,438×
4,511,347×
6,822,494×
7,388,482×
6,075,053×
6,581,645×
6,714,915×
5,525,113×
4,882,328×
6,207,253×
8,093,771×
6,845,558×
4,781,314×
4,151,471×
5,698,200×
5,755,045×
4,909,542×
6,065,104×
5,042,595×
4,667,497×
4,538,249×
3,982,484×
3,629,073×
3,920,749×
3,186,119×
2,364,898×
2,167,842×
1,819,862×
2,111,963×
1,282,322×
591,060×
547,385×
503,198×
399,639×
228,891×
93,208×
78,046×
105,360×
62,020×
26,286×
37,512×
33,484×
9,626×
2,405×

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0×
1×
552×
40,704×
142,268×
276,724×
311,692×
954,944×
1,311,669×
1,029,683×
3,963,644×
5,571,749×
4,732,609×
12,207,151×
14,120,196×
8,982,261×
7,067,927×
5,988,960×
8,232,266×
15,915,611×
22,824,377×
25,459,941×
22,332,945×
15,734,957×
18,187,923×
27,459,605×
32,240,772×
27,643,939×
30,999,725×
25,019,390×
19,924,051×
22,240,338×
21,029,517×
19,475,458×
18,738,132×
14,338,339×
11,777,540×
11,591,284×
10,167,748×
6,969,796×
6,105,916×
6,362,903×
7,375,958×
5,921,479×
4,294,253×
3,180,660×
2,616,681×
1,693,573×
1,382,312×
1,216,166×
704,785×
371,384×
286,325×
161,018×
91,735×
49,089×
13,149×
10,262×
21,656×
10,819×
1,376×
699×
64×

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0×
1×
624×
44,540×
332,400×
1,315,200×
5,138,517×
9,726,711×
6,337,439×
4,900,392×
7,505,620×
13,648,556×
19,623,604×
15,908,980×
18,414,581×
13,627,865×
14,338,314×
16,660,375×
20,137,777×
20,212,573×
17,943,282×
14,824,729×
17,961,758×
20,481,747×
19,531,736×
22,199,945×
20,593,821×
19,880,238×
18,035,099×
13,193,604×
17,282,814×
17,946,731×
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23,108,870×
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850,069×
688,463×
513,803×
300,699×
225,003×
178,164×
169,208×
56,217×
21,649×
12,058×
7,884×
3,332×
477×
1,131×
561×
48×

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0×
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564×
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24,843,222×
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2,228,943×
2,196,622×
2,260,585×
1,906,211×
1,575,730×
969,321×
561,717×
893,110×
867,625×
605,955×
522,513×
425,046×
409,707×
210,121×
370,426×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
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624×
42,656×
276,840×
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3,769,284×
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1,338,065×
4,074,671×
7,784,734×
7,473,794×
5,920,456×
4,699,549×
3,444,807×
2,831,896×
6,240,959×
16,634,007×
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38,713,888×
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843,668×
628,537×
195,411×
303,565×
550,116×
557,417×
503,566×
150,074×
111,270×
147,764×
199,618×
133,237×
38,021×
33,278×
27,906×
9,724×
11,472×
6,266×
6,820×
3,243×
5,836×
4,724×
845×
867×
99×
246×
251×
153×
53×
32×

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0×
1×
880×
78,100×
640,648×
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3,577,024×
4,910,060×
7,544,785×
12,319,185×
17,541,685×
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20,371,074×
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13,577,928×
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31,280,518×
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13,057,667×
13,475,744×
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651,340×
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751,520×
703,147×
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1,177,568×
740,455×
468,509×
815,064×
762,265×
543,935×
496,227×
387,534×
376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
1×
880×
81,264×
705,128×
1,416,596×
3,034,956×
7,032,272×
11,806,720×
11,380,068×
18,812,216×
16,835,023×
13,840,053×
11,256,527×
11,043,791×
14,979,687×
15,869,091×
23,109,214×
18,346,468×
18,659,492×
19,327,638×
25,941,446×
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28,088,932×
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36,873,539×
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27,041,833×
28,978,198×
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33,469,494×
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38,647,231×
42,073,168×
36,997,466×
31,839,031×
27,054,629×
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30,871,014×
28,146,242×
27,474,682×
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26,343,783×
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724,070×
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1,722,671×
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1,472,283×
651,340×
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2,259,390×
1,563,298×
1,271,957×
751,520×
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904,081×
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2,135,132×
2,780,405×
3,299,968×
2,490,003×
2,208,057×
2,274,186×
1,719,679×
1,239,441×
1,130,469×
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1,517,351×
1,400,033×
1,891,635×
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1,878,355×
1,484,699×
1,177,568×
740,455×
468,509×
815,064×
762,265×
543,935×
496,227×
387,534×
376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
1×
672×
45,100×
477,028×
2,692,824×
9,341,964×
9,878,836×
5,636,899×
7,001,363×
14,977,389×
15,227,689×
13,881,276×
15,438,083×
14,188,867×
13,152,902×
9,674,660×
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6,182,907×
6,542,466×
6,553,392×
5,661,996×
5,211,819×
3,830,331×
7,691,024×
18,579,456×
26,970,513×
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54,224,407×
56,644,178×
48,491,976×
37,529,782×
33,062,002×
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37,058,807×
61,943,136×
52,154,072×
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50,150,030×
59,684,113×
50,663,871×
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42,998,013×
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6,238,137×
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6,093,495×
5,171,904×
3,353,263×
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2,229,156×
1,514,650×
617,837×
493,320×
678,595×
767,250×
687,926×
292,314×
171,728×
244,558×
288,046×
167,285×
62,740×
78,476×
73,744×
32,163×
25,916×
10,451×
8,219×
4,461×
5,873×
4,724×
845×
867×
99×
246×
251×
153×
53×
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0×
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952×
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14,368,332×
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33,119,981×
36,066,204×
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387,534×
376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
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928×
81,512×
675,552×
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39,492,500×
28,434,197×
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29,745,180×
35,046,269×
38,814,721×
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165,074×
48,735×
17,418×
2,436×
360×

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360×

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751,520×
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1,878,355×
1,484,699×
1,177,568×
740,455×
468,509×
815,064×
762,265×
543,935×
496,227×
387,534×
376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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290,728×
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107,501,110×
90,747,018×
106,249,373×
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187,204,404×
219,649,882×
199,659,272×
210,002,204×
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186,814,646×
136,892,963×
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144,785,659×
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107,553,509×
103,948,285×
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121,522,967×
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123,850,563×
134,514,036×
126,361,476×
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107,298,546×
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104,955,985×
119,604,057×
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127,807,432×
112,837,967×
96,465,820×
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105,092,359×
119,856,980×
134,065,182×
141,425,075×
101,841,448×
102,381,556×
100,243,374×
99,895,962×
77,645,832×
69,382,066×
57,655,039×
46,142,107×
33,204,380×
27,164,138×
31,106,161×
23,866,680×
19,844,174×
21,812,300×
16,520,100×
12,789,655×
9,895,975×
9,842,142×
10,989,862×
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387,534×
376,223×
200,495×
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0×
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952×
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200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
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1,096×
119,076×
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65,394,227×
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299,864,604×
288,730,189×
273,344,637×
303,533,990×
308,712,943×
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292,033,319×
377,881,629×
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365,101,163×
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301,041,797×
274,102,843×
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740,455×
468,509×
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762,265×
543,935×
496,227×
387,534×
376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
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1,024×
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346,436,176×
297,722,578×
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169,785,085×
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200,495×
368,021×
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388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
1×
1,168×
125,268×
2,236,636×
27,657,660×
89,243,928×
99,410,612×
102,290,258×
352,976,785×
291,101,216×
300,242,290×
281,928,755×
232,502,612×
216,654,855×
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205,264,454×
210,875,742×
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166,269,747×
157,925,399×
195,294,616×
280,775,088×
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280,493,475×
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269,055,882×
228,154,282×
216,567,001×
256,935,923×
285,951,079×
298,967,560×
297,153,391×
320,749,354×
374,104,722×
426,907,067×
384,644,699×
385,114,092×
427,969,557×
418,281,307×
432,320,930×
436,779,336×
431,286,073×
470,610,641×
498,436,641×
490,937,957×
461,211,221×
395,325,896×
392,973,565×
322,053,544×
326,327,958×
372,020,705×
359,941,405×
366,424,424×
350,735,303×
363,706,353×
357,819,930×
370,337,335×
402,518,740×
422,045,421×
425,688,852×
388,982,206×
381,063,393×
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427,263,383×
408,179,691×
386,546,877×
376,100,528×
368,218,481×
338,568,013×
328,019,031×
352,732,599×
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274,025,620×
278,994,488×
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294,288,625×
270,308,037×
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290,976,415×
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257,813,479×
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126,611,449×
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55,707,963×
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1,484,699×
1,177,568×
740,455×
468,509×
815,064×
762,265×
543,935×
496,227×
387,534×
376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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165,074×
48,735×
17,418×
2,436×
360×

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0×
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1,424×
404,236×
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123,039,140×
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486,533,197×
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548,840,092×
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595,841,353×
543,025,221×
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614,729,281×
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711,300,923×
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547,894,387×
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378,419,450×
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376,223×
200,495×
368,021×
504,568×
388,506×
165,074×
48,735×
17,418×
2,436×
360×

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0×
1×
1,168×
330,540×
4,275,292×
17,383,128×
38,150,948×
90,550,332×
296,383,850×
504,258,848×
357,167,070×
720,540,589×
1,069,449,718×
750,143,606×
564,954,916×
610,945,837×
761,961,856×
1,069,484,868×
1,193,814,339×
1,466,422,648×
1,406,130,653×
1,206,830,126×
1,302,261,570×
1,217,904,441×
1,241,314,918×
1,363,235,428×
1,417,205,068×
1,208,123,437×
1,213,209,496×
1,300,273,896×
1,256,564,633×
1,129,468,892×
1,090,777,590×
1,040,167,141×
1,033,134,229×
944,151,458×
915,228,140×
861,184,755×
708,592,391×
641,698,434×
615,148,301×
575,908,365×
633,628,860×
742,703,955×
698,919,259×
731,845,041×
602,580,500×
731,293,683×
744,143,115×
664,107,635×
699,408,334×
597,946,750×
616,520,724×
727,457,549×
771,511,933×
645,797,907×
572,859,781×
474,665,751×
425,897,636×
434,544,194×
523,224,260×
469,644,481×
515,405,872×
492,920,183×
535,185,920×
504,192,386×
387,422,821×
384,561,979×
352,540,647×
276,778,618×
272,436,970×
318,253,775×
294,169,244×
247,040,942×
189,269,518×
158,501,164×
165,131,644×
157,754,354×
135,967,677×
171,292,053×
158,044,753×
152,782,719×
130,493,593×
158,134,037×
158,590,318×
103,001,744×
83,053,026×
68,742,182×
73,648,347×
67,482,373×
58,200,603×
64,029,575×
69,111,361×
62,678,248×
46,905,099×
40,599,331×
37,457,914×
39,556,541×
43,428,710×
33,143,675×
21,218,781×
17,737,359×
13,227,979×
13,240,563×
13,490,223×
11,827,097×
8,966,882×
7,634,978×
6,506,072×
6,259,047×
6,259,265×
4,334,834×
2,662,471×
1,533,363×
1,372,143×
1,172,419×
615,672×
291,390×
235,734×
155,314×
83,892×
57,981×
72,535×
19,821×
23,886×
11,937×
1,921×
887×
64×