Patterns Starting With 3
Patterns that can be factored: \[[3^*03^*_8]_n=3\cdot{8\cdot8^{2n}-7\cdot8^{n}-1\over7}=3\cdot\left(8^{n}-1\right)\left(8\cdot8^{n}+1\right)/7=3\cdot\left(7\cdot[1^*_8]_n\right)\left([10^*1_8]_n\right)/7\] \[[3^*63^*_8]_n=3\cdot{8\cdot8^{2n}+7\cdot8^{n}-1\over7}=3\cdot\left(8^{n}+1\right)\left(8\cdot8^{n}-1\right)/7=3\cdot\left([10^*1_8]_{n-1}\right)\left(7\cdot[1^*_8]_{n+1}\right)/7\] \[[3^*13^*_8]_n={24\cdot8^{2n}-14\cdot8^{n}-3\over7}=\left(4\cdot8^{n}-3\right)\left(6\cdot8^{n}+1\right)/7=\left([37^*5_8]_{n-1}\right)\left(7\cdot[6^*7_8]_{n-1}\right)/7\] \[[3^*53^*_8]_n={24\cdot8^{2n}+14\cdot8^{n}-3\over7}=\left(4\cdot8^{n}+3\right)\left(6\cdot8^{n}-1\right)/7=\left(7\cdot[4^*5_8]_{n-1}\right)\left([57^*_8]_n\right)/7\]
Links
> 30001: Quasi Repdigit 300..001
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> 30002: Quasi Repdigit 300..002
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> 30005: Quasi Repdigit 300..005
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> 30007: Quasi Repdigit 300..007
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> 31111: Near Repdigit 311..11
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> 31113: Depression 311..113
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> 31115: Quasi Repdigit 311..115
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> 31117: Quasi Repdigit 311..117
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> 31333: Near Repdigit 3133..33
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> 32221: Quasi Repdigit 322..221
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> 32223: Depression 322..223
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> 32225: Quasi Repdigit 322..225
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> 32226: Quasi Repdigit 322..226
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> 32227: Quasi Repdigit 322..227
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> 32333: Near Repdigit 3233..33
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> 33233: Near Repdigit Palindrome 33..33233..33
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> 33313: Near Repdigit 33..3313
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> 33323: Near Repdigit 33..3323
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> 33331: Near Repdigit 33..331
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> 33335: Near Repdigit 33..335
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> 33337: Near Repdigit 33..337
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> 33343: Near Repdigit 33..3343
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> 33353: Near Repdigit 33..3353
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> 33373: Near Repdigit 33..3373
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> 33433: Near Repdigit Palindrome 33..33433..33
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> 33733: Near Repdigit Palindrome 33..33733..33
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> 34333: Near Repdigit 3433..33
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> 34442: Quasi Repdigit 344..442
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> 34443: Plateau 344..443
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> 34445: Quasi Repdigit 344..445
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> 34447: Quasi Repdigit 344..447
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> 35333: Near Repdigit 3533..33
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> 35551: Quasi Repdigit 355..551
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> 35553: Plateau 355..553
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> 35555: Near Repdigit 355..55
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> 35557: Quasi Repdigit 355..557
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> 36661: Quasi Repdigit 366..661
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> 36662: Quasi Repdigit 366..662
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> 36665: Quasi Repdigit 366..665
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> 36667: Quasi Repdigit 366..667
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> 37333: Near Repdigit 3733..33
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> 37771: Quasi Repdigit 377..771
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> 37773: Plateau 377..773
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> 37775: Quasi Repdigit 377..775
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> 37777: Near Repdigit 377..77
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