Patterns Starting With 3
Patterns that can be factored: \[[3^*03^*_{10}]_n={10\cdot10^{2n}-9\cdot10^{n}-1\over3}=\left(10^{n}-1\right)\left(10\cdot10^{n}+1\right)/3=\left(9\cdot[1^*_{10}]_n\right)\left([10^*1_{10}]_n\right)/3\] \[[3^*63^*_{10}]_n={10\cdot10^{2n}+9\cdot10^{n}-1\over3}=\left(10^{n}+1\right)\left(10\cdot10^{n}-1\right)/3=\left([10^*1_{10}]_{n-1}\right)\left(9\cdot[1^*_{10}]_{n+1}\right)/3\] \[[3^*23^*_{10}]_n={10\cdot10^{2n}-3\cdot10^{n}-1\over3}=\left(2\cdot10^{n}-1\right)\left(5\cdot10^{n}+1\right)/3=\left([19^*_{10}]_n\right)\left(3\cdot[16^*7_{10}]_{n-1}\right)/3\] \[[3^*43^*_{10}]_n={10\cdot10^{2n}+3\cdot10^{n}-1\over3}=\left(2\cdot10^{n}+1\right)\left(5\cdot10^{n}-1\right)/3=\left(3\cdot[6^*7_{10}]_{n-1}\right)\left([49^*_{10}]_n\right)/3\]
Links
> 30001: Quasi Repdigit 300..001
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> 30002: Quasi Repdigit 300..002
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> 30004: Quasi Repdigit 300..004
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> 30007: Quasi Repdigit 300..007
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> 30008: Quasi Repdigit 300..008
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> 31111: Near Repdigit 311..11
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> 31113: Depression 311..113
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> 31117: Quasi Repdigit 311..117
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> 31119: Quasi Repdigit 311..119
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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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> 32224: Quasi Repdigit 322..224
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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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> 32228: Quasi Repdigit 322..228
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> 32229: Quasi Repdigit 322..229
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> 32333: Near Repdigit 3233..33
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> 33133: Near Repdigit Palindrome 33..33133..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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> 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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> 33383: Near Repdigit 33..3383
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> 33533: Near Repdigit Palindrome 33..33533..33
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> 33733: Near Repdigit Palindrome 33..33733..33
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> 33833: Near Repdigit Palindrome 33..33833..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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> 34444: Near Repdigit 344..44
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> 34446: Quasi Repdigit 344..446
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> 34447: Quasi Repdigit 344..447
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> 34448: Quasi Repdigit 344..448
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> 34449: Quasi Repdigit 344..449
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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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> 35557: Quasi Repdigit 355..557
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> 35559: Quasi Repdigit 355..559
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> 36661: Quasi Repdigit 366..661
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> 36662: Quasi Repdigit 366..662
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> 36664: Quasi Repdigit 366..664
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> 36667: Quasi Repdigit 366..667
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> 36668: Quasi Repdigit 366..668
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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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> 37777: Near Repdigit 377..77
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> 37779: Quasi Repdigit 377..779
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> 38333: Near Repdigit 3833..33
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> 38881: Quasi Repdigit 388..881
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> 38882: Quasi Repdigit 388..882
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> 38883: Plateau 388..883
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> 38884: Quasi Repdigit 388..884
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> 38887: Quasi Repdigit 388..887
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> 38888: Near Repdigit 388..88
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> 38889: Quasi Repdigit 388..889
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> 39991: Quasi Repdigit 399..991
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> 39997: Quasi Repdigit 399..997
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