Patterns Starting With 2
Patterns that can be factored: \[[2^*02^*_7]_n={7\cdot7^{2n}-6\cdot7^{n}-1\over3}=\left(7^{n}-1\right)\left(7\cdot7^{n}+1\right)/3=\left(6\cdot[1^*_7]_n\right)\left(2\cdot[3^*4_7]_n\right)/3\] \[[2^*42^*_7]_n={7\cdot7^{2n}+6\cdot7^{n}-1\over3}=\left(7^{n}+1\right)\left(7\cdot7^{n}-1\right)/3=\left(2\cdot[3^*4_7]_{n-1}\right)\left(6\cdot[1^*_7]_{n+1}\right)/3\]
Links
> 20003: Quasi Repdigit 200..003
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> 20005: Quasi Repdigit 200..005
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> 21111: Near Repdigit 211..11
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> 21112: Depression 211..112
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> 21113: Quasi Repdigit 211..113
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> 21114: Quasi Repdigit 211..114
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> 21115: Quasi Repdigit 211..115
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> 21116: Quasi Repdigit 211..116
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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
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> 22223: Near Repdigit 22..223
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> 22225: Near Repdigit 22..225
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> 22232: Near Repdigit 22..2232
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> 22252: Near Repdigit 22..2252
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> 22322: Near Repdigit Palindrome 22..22322..22
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> 22522: Near Repdigit Palindrome 22..22522..22
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> 23222: Near Repdigit 2322..22
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> 23332: Plateau 233..332
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> 23333: Near Repdigit 233..33
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> 23335: Quasi Repdigit 233..335
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> 24441: Quasi Repdigit 244..441
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> 24443: Quasi Repdigit 244..443
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> 24445: Quasi Repdigit 244..445
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> 25222: Near Repdigit 2522..22
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> 25551: Quasi Repdigit 255..551
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> 25552: Plateau 255..552
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> 25554: Quasi Repdigit 255..554
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> 25555: Near Repdigit 255..55
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> 25556: Quasi Repdigit 255..556
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> 26663: Quasi Repdigit 266..663
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> 26665: Quasi Repdigit 266..665
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