Base 3
Patterns that can be factored: \[[1^*01^*_3]_n={3\cdot3^{2n}-2\cdot3^{n}-1\over2}=\left(3^{n}-1\right)\left(3\cdot3^{n}+1\right)/2=\left(2\cdot[1^*_3]_n\right)\left(2\cdot[1^*2_3]_n\right)/2\] \[[1^*21^*_3]_n={3\cdot3^{2n}+2\cdot3^{n}-1\over2}=\left(3^{n}+1\right)\left(3\cdot3^{n}-1\right)/2=\left(2\cdot[1^*2_3]_{n-1}\right)\left(2\cdot[1^*_3]_{n+1}\right)/2\] \[[2^*02^*_3]_n=3\cdot3^{2n}-2\cdot3^{n}-1=\left(3^{n}-1\right)\left(3\cdot3^{n}+1\right)=\left(2\cdot[1^*_3]_n\right)\left(2\cdot[1^*2_3]_n\right)\]
Links
> 10002: Quasi Repdigit 100..002
(table)
> 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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> 11121: Near Repdigit 11..1121
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> 12111: Near Repdigit 1211..11
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> 12222: Near Repdigit 122..22
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> 20001: Quasi Repdigit 200..001
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> 21111: Near Repdigit 211..11
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> 21112: Depression 211..112
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> 21222: Near Repdigit 2122..22
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> 22122: Near Repdigit Palindrome 22..22122..22
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> 22212: Near Repdigit 22..2212
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> 22221: Near Repdigit 22..221
(table)