45#唯一周期素数（10^3750-1）/9的φ因子

yangchuanju

OEIS网站的网页A040017给出46个一路增大的（10^n-1）/9的φ因子（唯一周期素数），其中45#为（10^1031-1）/9的φ因子（111…1<p1031>）；而网页A0511627给出的45#φ因子对应指数号是3750、46#φ因子的指数号才是1031；经多方核对，发现两网页在此发生错乱，A040017的45#应改为46#，46#应改为47#，需增加一个新的45#φ因子（p1001）。

（10^3750-1）/9的1001位φ因子（唯一因子）已经求算出来，结构如下：1+125个0+249个9+8+124个9+8+125个9+249个0+1+124个0+1

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000099999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001——1001位

yangchuanju

A040017
Unique period primes (no other prime has same period as 1/p) in order (periods are given in A051627).
3, 11, 37, 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991, 909090909090909090909090909091，……

# This is the b040017.txt text file.
# A040017: Unique period primes (no other prime has same period as 1/p) in order (periods are given in A051627).
# Dated 20 June 2015.

1  3
2  11
3  37
4  101
5  9091
6  9901
7  333667
8  909091
9  99990001
10  999999000001
11  9999999900000001
12  909090909090909091
13  1111111111111111111
14  11111111111111111111111
15  900900900900990990990991
16  909090909090909090909090909091
17  100009999999899989999000000010001
18  10000099999999989999899999000000000100001
19  9090909090909090909090909090909090909090909090909091
20  900900900900900900900900900900990990990990990990990990990991
21  909090909090909090909090909090909090909090909090909090909090909091
22  142857157142857142856999999985714285714285857142857142855714285571428571428572857143
23  999999999999990000000000000099999999999999000000000000009999999999999900000000000001
24  99999999999999999999999999999999000000000000000000000000000000009999999999999999999999999999999900000000000000000000000000000001
25  1098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098900989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011
26  1000999998999000001000999998999000001000999998999000001000999998999000001000999998999000001000999998999000001000999998998999000001000999998999000001000999998999000001000999998999000001000999998999000001000999998999000001000999998999000001001
27  1111099888878889001111100000000000011110998888788890011222109988887889011221109998887788901111110999878890112222210987766677901122222109888790001111110988877889000111221098887888900112221099888878889001111100000000000011110998888788890011111
28  9090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909091
29  11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
30  900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900900990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990990991
31  1000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000001
32  1000000001000000000999999999999999999999999998999999998999999997999999998999999999000000000000000000000000001000000001000000001000000001000000001000000000999999999999999999999999998999999999999999998999999999999999998999999999999999998999999999999999999000000000000000000000000001000000001000000001000000001000000001000000000999999999999999999999999998999999998999999997999999998999999999000000000000000000000000001000000001000000001
33  100000000000000000000009999999999999999999999999999999999999999999899999999999999999999990000000000000000000000000000000000000000000100000000000000000000009999999999999999999999999999999999999999999899999999999999999999989999999999999999999999000000000000000000000000000000000000000000010000000000000000000000999999999999999999999999999999999999999999989999999999999999999999000000000000000000000000000000000000000000010000000000000000000001
34  1000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000000999999999999999999999999999999999998999999999999999998999999999999999999000000000000000000000000000000000001000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000000999999999999999999999999999999999998999999999999999999000000000000000000000000000000000001000000000000000001
35  1000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000001000099999998999900000000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010000999999989999000000010001
36  99009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009901
37  1009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990001009998990000999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000100999899000101
38  9090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909091
39  1099999999999999999999988999999890000000000000110000001100000010999998899999988999999890000009900000110000001099999900999999009999989000000990000009900000098999990099999900999999010000100100000990000009899998998999989989999901000010010000100100001000999899899998998999989990000999900010010000100099990000999900009998999000099990000999900009998999000099990000999900010010000100099990000999899899998998999989990001001000010010000100100000989999899899998998999990099999901000010010000099000000990000009899999009999990099999900999998900000099000000990000011000000109999990099999889999998899999989000001100000011000000109999999999999889999998900000000000000000000011
40  1000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000000999999999999999999999998999999999999000000000000000000000001000000000001
41  1000000099999999999999999999999999999999999999999899999990000000000000000000000000000000000000000010000000999999999999999999999999999899999989999998999999900000000000000000000000000010000001000000100000009999999999999999999999999998999999899999989999999000000000000010000001000000100000010000001000000099999999999998999999899999989999998999999899999990000000000000100000010000001000000100000009999999999999899999989999998999999899999989999999000000000000010000001000000100000010000001000000099999999999998999999899999989999999000000000000000000000000000100000010000001000000099999999999999999999999999989999998999999899999990000000000000000000000000001000000099999999999999999999999999999999999999999899999990000000000000000000000000000000000000000010000001
42  99009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009901
43  999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000001
44  1099999999989000000000109999999998900000000010999999999890000000001099999999989000000000109999999888900000001110999999988890000000111099999998889000000011109999999888900000001110999999988890000011111099999888889000001111109999988888900000111110999998888890000011111099999888889000001111109998888888900011111110999888888890001111111099988888889000111111109998888888900011111110999888888890111111111098888888889011111111109888888888901111111110988888888890111111111098888888889011111111098888888889011111111109888888888901111111110988888888890111111111098888888889011111111109888888890001111111099988888889000111111109998888888900011111110999888888890001111111099988888889000111110999998888890000011111099999888889000001111109999988888900000111110999998888890000011111099999888900000001110999999988890000000111099999998889000000011109999999888900000001110999999988890000000109999999998900000000010999999999890000000001099999999989000000000109999999998900000000011
45  11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
46  999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990000999900009999000099990001

yangchuanju

A051627  Periods associated with A040017.
1, 2, 3, 4, 10, 12, 9, 14, 24, 36, 48, 38, 19, 23, 39, 62, 120, 150, 106, 93, 134, 294, 196, 320, 654, 738, 385, 586, 317, 597, 1404, 945, 1452, 1836, 1752, 1172, 1812, 1282, 1426, 2232, 1862, 1844, 1521, 2134, 3750, 1031, 2264, 2667, 4354, 3927, 4274, 6522, 3903, 6022, 6682, 6135, 9550, 5877，……

# b051627.txt - Table of n, a(n) for n=1..99 - Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 23 2010
1 1
2 2
3 3
4 4
5 10
6 12
7 9
8 14
9 24
10 36
11 48
12 38
13 19
14 23
15 39
16 62
17 120
18 150
19 106
20 93
21 134
22 294
23 196
24 320
25 654
26 738
27 385
28 586
29 317
30 597
31 1404
32 945
33 1452
34 1836
35 1752
36 1172
37 1812
38 1282
39 1426
40 2232
41 1862
42 1844
43 1521
44 2134
45 3750
46 1031
47 2264
48 2667
49 4354
50 3927
51 4274
52 6522
53 3903
54 6022
55 6682
56 6135
57 9550
58 5877
59 15456
60 8696
61 13092
62 13370
63 6437
64 14714
65 10887
66 19240
67 23664
68 18910
69 24174
70 18668
71 36630
72 20644
73 23912
74 26570
75 40120
76 47184
77 52062
78 18827
79 59772
80 47498
81 79710
82 32481
83 70842
84 47468
85 73094
86 92712
87 82360
88 73808
89 92092
90 68102
91 103248
92 88676
93 100480
94 55601
95 145878
96 49081
97 141230
98 77077
99 198552

yangchuanju

(10^3750-1)/9分解式  
内含49个素因子和3个复合因子
R3750 = (10^3750-1)/9 = 1111111111...<3750> = 3 × 7 × 11 × 13 × 31 × 37 × 41 × 151 × 211 × 241 × 251 × 271 × 751 × 2161 × 4201 × 5051 × 9091 × 21001 × 21401 × 21751 × 25601 × 160001 × 162251 × 2906161 × 47001751 × 1797655751<10> × 10893295001<11> × 107205285001<12> × 182521213001<12> × 4471031976001<13> × 50779597795001<14> × 78875943472201<14> × 176144543406001<15> × 128372635774581251<18> × 2071431405211934430001<22> × 4367691100790232228751<22> × 25005172023963824973001<23> × 76910683502000715393525001<26> × 59244397795882902986928930001<29> × 15763985553739191709164170940063151<35> × 1000009999999998999989999900000000010000<41> × 2782057126261476352728985117193142348250001<43> × 1375436107164906400113195032668541009729549504205143102033627145732751<70> × 4709825349852110182615878875374419529306990314325041101342026868334001<70> × 42051775804956304559810859008305819975199677041099230574273451704628125001<74> × 14332371646347867103751140722104256371688921437307256086517631268211025054763001<80> × 269409792871731627664586194662281233853701011108906726055753272681082282441709251<81> × 15905910605959927957520599214257369978644811514228442375715283978375304416453709933630691450134077795142751<107> × [3594462495...<C458>] × [9587725422...<C464>] × [1340524207...<C921>] × 1000000000...<P1001>(50.88%)