Patterns Starting With 1
Patterns that can be factored: \[[1^*01^*_9]_n={9\cdot9^{2n}-8\cdot9^{n}-1\over8}=\left(9^{n}-1\right)\left(9\cdot9^{n}+1\right)/8=\left(8\cdot[1^*_9]_n\right)\left(2\cdot[4^*5_9]_n\right)/8\] \[[1^*21^*_9]_n={9\cdot9^{2n}+8\cdot9^{n}-1\over8}=\left(9^{n}+1\right)\left(9\cdot9^{n}-1\right)/8=\left(2\cdot[4^*5_9]_{n-1}\right)\left(8\cdot[1^*_9]_{n+1}\right)/8\]
Links
> 10002: Quasi Repdigit 100..002
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> 10004: Quasi Repdigit 100..004
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> 10008: Quasi Repdigit 100..008
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> 10111: Near Repdigit 1011..11
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> 11101: Near Repdigit 11..1101
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> 11111: Repunit 11..11
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> 11112: Near Repdigit 11..112
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> 11114: Near Repdigit 11..114
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> 11115: Near Repdigit 11..115
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> 11117: Near Repdigit 11..117
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> 11118: Near Repdigit 11..118
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> 11121: Near Repdigit 11..1121
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> 11131: Near Repdigit 11..1131
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> 11141: Near Repdigit 11..1141
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> 11151: Near Repdigit 11..1151
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> 11161: Near Repdigit 11..1161
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> 11171: Near Repdigit 11..1171
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> 11181: Near Repdigit 11..1181
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> 11311: Near Repdigit Palindrome 11..11311..11
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> 11411: Near Repdigit Palindrome 11..11411..11
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> 11511: Near Repdigit Palindrome 11..11511..11
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> 11611: Near Repdigit Palindrome 11..11611..11
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> 11711: Near Repdigit Palindrome 11..11711..11
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> 11811: Near Repdigit Palindrome 11..11811..11
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> 12111: Near Repdigit 1211..11
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> 12222: Near Repdigit 122..22
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> 12224: Quasi Repdigit 122..224
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> 12228: Quasi Repdigit 122..228
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> 13111: Near Repdigit 1311..11
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> 13331: Plateau 133..331
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> 13334: Quasi Repdigit 133..334
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> 13335: Quasi Repdigit 133..335
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> 13337: Quasi Repdigit 133..337
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> 13338: Quasi Repdigit 133..338
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> 14111: Near Repdigit 1411..11
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> 14442: Quasi Repdigit 144..442
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> 14444: Near Repdigit 144..44
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> 14448: Quasi Repdigit 144..448
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> 15111: Near Repdigit 1511..11
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> 15551: Plateau 155..551
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> 15552: Quasi Repdigit 155..552
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> 15555: Near Repdigit 155..55
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> 15557: Quasi Repdigit 155..557
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> 15558: Quasi Repdigit 155..558
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> 16111: Near Repdigit 1611..11
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> 16662: Quasi Repdigit 166..662
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> 16664: Quasi Repdigit 166..664
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> 16668: Quasi Repdigit 166..668
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> 17111: Near Repdigit 1711..11
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> 17772: Quasi Repdigit 177..772
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> 17774: Quasi Repdigit 177..774
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> 17775: Quasi Repdigit 177..775
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> 17777: Near Repdigit 177..77
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> 17778: Quasi Repdigit 177..778
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> 18111: Near Repdigit 1811..11
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> 18882: Quasi Repdigit 188..882
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> 18884: Quasi Repdigit 188..884
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> 18888: Near Repdigit 188..88
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