## Solutions of infinite pattern

(last update : August 03, 2008)

For 2 digits, the followings are infinite patterns.

• 102n
• 4 * 102n
• 9 * 102n

### The solutions of infinite pattern for 3 digits

No.ab=a2digits
1 uppermost and lowermost digit is 1,
and properly arranged 0, 1.
101
1001
1011
1101
10001
uppermost and lowermost digit is 1,
and properly arranged 0, 1.
10201
1002001
1022121
1212201
100020001
012
2 1010000104010000101
101000001040100000101

100010100040001010001
numbers of "0" between "1" and "1",
and "1" and "4" is odd number.
1020100210100211022100121010020010201
10201000210100201102210010210100200010201

10002020110011010022202101001100102020001
012
3 102
1002
10002
100002
1000002
10404
1004004
100040004
10000400004
1000004000004
014
4 201
2001
20001
200001
2000001
40401
4004001
400040001
40000400001
4000004000001
014
5 uppermost and lowermost digit is 1,
and properly arranged 0, 1, 2.
10200201
100202001
102000201
1020000201
uppermost and lowermost digit is 1,
and properly arranged 0, 1, 4.
104044100440401
10040441004404001
10404041004040401
1040400410040040401
014
6 uppermost and lowermost digit is 2,
and properly arranged 0, 1, 2.
20100102
200101002
201000102
2010000102
uppermost and lowermost digit is 4,
and properly arranged 0, 1, 4.
404014100410404
40040411001404004
40401041004010404
4040100410040010404
014
7 10301
1003001
100030001
106110601
1006011006001
10006001100060001
016
8 10801
1008001
100080001
116661601
1016066016001
10016006600160001
016
9 40012700004
4000127000004
400001270000004
1601016161610101600016
16001016016161001016000016
160001016001616100010160000016
016
10 901
9001
90001
900001
9000001
811801
81018001
8100180001
810001800001
81000018000001
018
11 1009
10009
100009
1000009
10000009
1018081
100180081
10001800081
1000018000081
100000180000081
018
12 10401
1004001
100040001
108180801
1008018008001
10008001800080001
018
13 100901
10009001
1000090001
10181011801
100180101018001
1000180010100180001
018
14 20602
2006002
200060002
424442404
4024044024004
40024004400240004
024
15 uppermost and lowermost digit is 5,
and properly arranged 0, 5.
505
5005
50005
500005
500505
uppermost and lowermost digits are 25,
and properly arranged 0, 2, 5.
255025
25050025
2500500025
250005000025
250505255025
025
16 15008515
150000850015
1500000085000015
225255522505225
22500255005222525500225
2250000255000052225002550000225
025
17 8000254000008
800002540000008
64004064064644004064000064
640004064006464400040640000064
046
18 uppermost and lowermost digit is 2,
and properly arranged 0, 2.
202
2002
2022
2202
20002
uppermost and lowermost digit is 4,
and properly arranged 0, 4, 8.
40804
4008004
4088484
4848804
400080004
048
19 97
997
9997
99997
999997
9409
994009
99940009
9999400009
999994000009
049
20 20102
2001002
200010002
404090404
4004009004004
40004000900040004
049
21 338
3338
33338
333338
3333338
114244
11142244
1111422244
111114222244
11111142222244
124
22 335
3335
33335
333335
3333335
112225
11122225
1111222225
111112222225
11111122222225
125
23 1235
12335
123335
1233335
12333335
1525225
152152225
15211522225
1521115222225
152111152222225
125
24 3333504485
33333504485
333333504485
11112252151515115225
1111122521251515115225
111111225212251515115225
125
25 359
3359
33359
333359
3333359
128881
11282881
1112822881
111128222881
11111282222881
128
26 334
3334
33334
333334
3333334
111556
11115556
1111155556
111111555556
11111115555556
156
27 665
6665
66665
666665
6666665
442225
44422225
4444222225
444442222225
44444422222225
245
28 6515
66515
666515
6666515
66666515
42445225
4424245225
444242245225
44442422245225
4444424222245225
245
29 2335
23335
233335
2333335
23333335
5452225
544522225
54445222225
5444452222225
544444522222225
245
30 668
6668
66668
666668
6666668
446224
44462224
4444622224
444446222224
44444462222224
246
31 165
1665
16665
166665
1666665
27225
2772225
277722225
27777222225
2777772222225
257
32 667
6667
66667
666667
6666667
444889
44448889
4444488889
444444888889
44444448888889
489

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima