Patterns Starting With 6
Patterns that can be factored: \[[6^*06^*_8]_n=6\cdot{8\cdot8^{2n}-7\cdot8^{n}-1\over7}=6\cdot\left(8^{n}-1\right)\left(8\cdot8^{n}+1\right)/7=6\cdot\left(7\cdot[1^*_8]_n\right)\left([10^*1_8]_n\right)/7\] \[[6^*26^*_8]_n=2\cdot{24\cdot8^{2n}-14\cdot8^{n}-3\over7}=2\cdot\left(4\cdot8^{n}-3\right)\left(6\cdot8^{n}+1\right)/7=2\cdot\left([37^*5_8]_{n-1}\right)\left(7\cdot[6^*7_8]_{n-1}\right)/7\]
Links
> 60005: Quasi Repdigit 600..005
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> 60007: Quasi Repdigit 600..007
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> 61111: Near Repdigit 611..11
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> 61112: Quasi Repdigit 611..112
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> 61113: Quasi Repdigit 611..113
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> 61114: Quasi Repdigit 611..114
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> 61115: Quasi Repdigit 611..115
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> 61116: Depression 611..116
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> 61117: Quasi Repdigit 611..117
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> 61666: Near Repdigit 6166..66
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> 62221: Quasi Repdigit 622..221
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> 62223: Quasi Repdigit 622..223
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> 62225: Quasi Repdigit 622..225
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> 63331: Quasi Repdigit 633..331
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> 63334: Quasi Repdigit 633..334
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> 63335: Quasi Repdigit 633..335
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> 64441: Quasi Repdigit 644..441
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> 64443: Quasi Repdigit 644..443
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> 64445: Quasi Repdigit 644..445
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> 64447: Quasi Repdigit 644..447
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> 65551: Quasi Repdigit 655..551
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> 65552: Quasi Repdigit 655..552
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> 65553: Quasi Repdigit 655..553
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> 65554: Quasi Repdigit 655..554
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> 65555: Near Repdigit 655..55
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> 65556: Depression 655..556
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> 65557: Quasi Repdigit 655..557
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> 65666: Near Repdigit 6566..66
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> 66166: Near Repdigit Palindrome 66..66166..66
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> 66566: Near Repdigit Palindrome 66..66566..66
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> 66616: Near Repdigit 66..6616
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> 66656: Near Repdigit 66..6656
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> 66661: Near Repdigit 66..661
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> 66665: Near Repdigit 66..665
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> 66667: Near Repdigit 66..667
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> 66766: Near Repdigit Palindrome 66..66766..66
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> 67666: Near Repdigit 6766..66
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> 67772: Quasi Repdigit 677..772
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> 67773: Quasi Repdigit 677..773
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> 67774: Quasi Repdigit 677..774
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> 67775: Quasi Repdigit 677..775
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> 67776: Plateau 677..776
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> 67777: Near Repdigit 677..77
(table)