Patterns Starting With 1
Patterns that can be factored: \[[1^*01^*_{10}]_n={10\cdot10^{2n}-9\cdot10^{n}-1\over9}=\left(10^{n}-1\right)\left(10\cdot10^{n}+1\right)/9=\left(9\cdot[1^*_{10}]_n\right)\left([10^*1_{10}]_n\right)/9\] \[[1^*21^*_{10}]_n={10\cdot10^{2n}+9\cdot10^{n}-1\over9}=\left(10^{n}+1\right)\left(10\cdot10^{n}-1\right)/9=\left([10^*1_{10}]_{n-1}\right)\left(9\cdot[1^*_{10}]_{n+1}\right)/9\]
Links
> 10001: Depression 100..001
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> 10003: Quasi Repdigit 100..003
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> 10004: Quasi Repdigit 100..004
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> 10007: Quasi Repdigit 100..007
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> 10009: Quasi Repdigit 100..009
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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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> 11113: Near Repdigit 11..113
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> 11117: Near Repdigit 11..117
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> 11119: Near Repdigit 11..119
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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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> 11191: Near Repdigit 11..1191
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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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> 11911: Near Repdigit Palindrome 11..11911..11
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> 12111: Near Repdigit 1211..11
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> 12223: Quasi Repdigit 122..223
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> 12224: Quasi Repdigit 122..224
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> 12227: Quasi Repdigit 122..227
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> 12228: Quasi Repdigit 122..228
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> 12229: Quasi Repdigit 122..229
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> 13111: Near Repdigit 1311..11
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> 13331: Plateau 133..331
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> 13333: Near Repdigit 133..33
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> 13337: Quasi Repdigit 133..337
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> 13339: Quasi Repdigit 133..339
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> 14111: Near Repdigit 1411..11
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> 14441: Plateau 144..441
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> 14444: Near Repdigit 144..44
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> 14447: Quasi Repdigit 144..447
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> 14448: Quasi Repdigit 144..448
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> 14449: Quasi Repdigit 144..449
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> 15111: Near Repdigit 1511..11
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> 15551: Plateau 155..551
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> 15553: Quasi Repdigit 155..553
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> 15557: Quasi Repdigit 155..557
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> 15559: Quasi Repdigit 155..559
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> 16111: Near Repdigit 1611..11
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> 16661: Plateau 166..661
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> 16663: Quasi Repdigit 166..663
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> 16664: Quasi Repdigit 166..664
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> 16667: Quasi Repdigit 166..667
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> 16669: Quasi Repdigit 166..669
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> 17111: Near Repdigit 1711..11
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> 17771: Plateau 177..771
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> 17773: Quasi Repdigit 177..773
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> 17777: Near Repdigit 177..77
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> 17779: Quasi Repdigit 177..779
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> 18111: Near Repdigit 1811..11
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> 18881: Plateau 188..881
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> 18883: Quasi Repdigit 188..883
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> 18884: Quasi Repdigit 188..884
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> 18888: Near Repdigit 188..88
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> 18889: Quasi Repdigit 188..889
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> 19111: Near Repdigit 1911..11
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> 19991: Plateau 199..991
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> 19993: Quasi Repdigit 199..993
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> 19997: Quasi Repdigit 199..997
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> 19999: Near Repdigit 199..99
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