Patterns Starting With 1
Patterns that can be factored: \[[1^*01^*_8]_n={8\cdot8^{2n}-7\cdot8^{n}-1\over7}=\left(8^{n}-1\right)\left(8\cdot8^{n}+1\right)/7=\left(7\cdot[1^*_8]_n\right)\left([10^*1_8]_n\right)/7\] \[[1^*21^*_8]_n={8\cdot8^{2n}+7\cdot8^{n}-1\over7}=\left(8^{n}+1\right)\left(8\cdot8^{n}-1\right)/7=\left([10^*1_8]_{n-1}\right)\left(7\cdot[1^*_8]_{n+1}\right)/7\]
Links
> 10001: Depression 100..001
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> 10003: Quasi Repdigit 100..003
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> 10005: Quasi Repdigit 100..005
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> 10007: Quasi Repdigit 100..007
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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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> 11113: Near Repdigit 11..113
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> 11115: Near Repdigit 11..115
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> 11117: Near Repdigit 11..117
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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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> 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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> 12111: Near Repdigit 1211..11
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> 12223: Quasi Repdigit 122..223
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> 12225: Quasi Repdigit 122..225
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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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> 13335: Quasi Repdigit 133..335
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> 14111: Near Repdigit 1411..11
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> 14441: Plateau 144..441
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> 14445: Quasi Repdigit 144..445
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> 14447: Quasi Repdigit 144..447
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> 15111: Near Repdigit 1511..11
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> 15553: Quasi Repdigit 155..553
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> 15555: Near Repdigit 155..55
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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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> 16667: Quasi Repdigit 166..667
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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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> 17775: Quasi Repdigit 177..775
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> 17777: Near Repdigit 177..77
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