For 2 digits, the followings are infinite patterns.
(The solutions of sporadic pattern are here.)
| No. | a | b=a2 | digits |
|---|---|---|---|
| 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 |
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