Patterns Starting With 4
Patterns that can be factored: \[[4^*04^*_7]_n=2\cdot{7\cdot7^{2n}-6\cdot7^{n}-1\over3}=2\cdot\left(7^{n}-1\right)\left(7\cdot7^{n}+1\right)/3=2\cdot\left(6\cdot[1^*_7]_n\right)\left(2\cdot[3^*4_7]_n\right)/3\] \[[4^*34^*_7]_n={14\cdot7^{2n}-3\cdot7^{n}-2\over3}=\left(2\cdot7^{n}-1\right)\left(7\cdot7^{n}+2\right)/3=\left([16^*_7]_n\right)\left(3\cdot[2^*3_7]_n\right)/3\] \[[4^*54^*_7]_n={14\cdot7^{2n}+3\cdot7^{n}-2\over3}=\left(2\cdot7^{n}+1\right)\left(7\cdot7^{n}-2\right)/3=\left(3\cdot[4^*5_7]_{n-1}\right)\left([6^*5_7]_n\right)/3\]
Links
> 40001: Quasi Repdigit 400..001
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> 40003: Quasi Repdigit 400..003
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> 41111: Near Repdigit 411..11
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> 41113: Quasi Repdigit 411..113
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> 41114: Depression 411..114
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> 41115: Quasi Repdigit 411..115
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> 41116: Quasi Repdigit 411..116
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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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> 43331: Quasi Repdigit 433..331
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> 43333: Near Repdigit 433..33
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> 43334: Depression 433..334
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> 43336: Quasi Repdigit 433..336
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> 43444: Near Repdigit 4344..44
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> 44144: Near Repdigit Palindrome 44..44144..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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> 44443: Near Repdigit 44..443
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> 44445: Near Repdigit 44..445
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> 44454: Near Repdigit 44..4454
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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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> 46661: Quasi Repdigit 466..661
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> 46663: Quasi Repdigit 466..663
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