Patterns Starting With 4
Patterns that can be factored: \[[4^*04^*_9]_n={9\cdot9^{2n}-8\cdot9^{n}-1\over2}=\left(9^{n}-1\right)\left(9\cdot9^{n}+1\right)/2=\left(8\cdot[1^*_9]_n\right)\left(2\cdot[4^*5_9]_n\right)/2\] \[[4^*84^*_9]_n={9\cdot9^{2n}+8\cdot9^{n}-1\over2}=\left(9^{n}+1\right)\left(9\cdot9^{n}-1\right)/2=\left(2\cdot[4^*5_9]_{n-1}\right)\left(8\cdot[1^*_9]_{n+1}\right)/2\]
Links
> 40001: Quasi Repdigit 400..001
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> 40003: Quasi Repdigit 400..003
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> 40005: Quasi Repdigit 400..005
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> 40007: Quasi Repdigit 400..007
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> 41111: Near Repdigit 411..11
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> 41112: Quasi Repdigit 411..112
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> 41114: Depression 411..114
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> 41115: Quasi Repdigit 411..115
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> 41117: Quasi Repdigit 411..117
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> 41444: Near Repdigit 4144..44
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> 42221: Quasi Repdigit 422..221
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> 42223: Quasi Repdigit 422..223
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> 42225: Quasi Repdigit 422..225
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> 42227: Quasi Repdigit 422..227
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> 43331: Quasi Repdigit 433..331
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> 43332: Quasi Repdigit 433..332
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> 43335: Quasi Repdigit 433..335
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> 43337: Quasi Repdigit 433..337
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> 43338: Quasi Repdigit 433..338
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> 43444: Near Repdigit 4344..44
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> 44144: Near Repdigit Palindrome 44..44144..44
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> 44344: Near Repdigit Palindrome 44..44344..44
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> 44414: Near Repdigit 44..4414
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> 44434: Near Repdigit 44..4434
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> 44441: Near Repdigit 44..441
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> 44445: Near Repdigit 44..445
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> 44447: Near Repdigit 44..447
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> 44454: Near Repdigit 44..4454
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> 44474: Near Repdigit 44..4474
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> 44544: Near Repdigit Palindrome 44..44544..44
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> 44744: Near Repdigit Palindrome 44..44744..44
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> 45444: Near Repdigit 4544..44
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> 45552: Quasi Repdigit 455..552
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> 45553: Quasi Repdigit 455..553
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> 45554: Plateau 455..554
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> 45555: Near Repdigit 455..55
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> 45556: Quasi Repdigit 455..556
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> 45557: Quasi Repdigit 455..557
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> 45558: Quasi Repdigit 455..558
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> 46661: Quasi Repdigit 466..661
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> 46663: Quasi Repdigit 466..663
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> 46665: Quasi Repdigit 466..665
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> 46667: Quasi Repdigit 466..667
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> 47444: Near Repdigit 4744..44
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> 47771: Quasi Repdigit 477..771
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> 47772: Quasi Repdigit 477..772
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> 47774: Plateau 477..774
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> 47775: Quasi Repdigit 477..775
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> 47777: Near Repdigit 477..77
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> 47778: Quasi Repdigit 477..778
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> 48881: Quasi Repdigit 488..881
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> 48883: Quasi Repdigit 488..883
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> 48885: Quasi Repdigit 488..885
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> 48887: Quasi Repdigit 488..887
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