Patterns Starting With 1
Patterns that can be factored: \[[1^*01^*_7]_n={7\cdot7^{2n}-6\cdot7^{n}-1\over6}=\left(7^{n}-1\right)\left(7\cdot7^{n}+1\right)/6=\left(6\cdot[1^*_7]_n\right)\left(2\cdot[3^*4_7]_n\right)/6\] \[[1^*21^*_7]_n={7\cdot7^{2n}+6\cdot7^{n}-1\over6}=\left(7^{n}+1\right)\left(7\cdot7^{n}-1\right)/6=\left(2\cdot[3^*4_7]_{n-1}\right)\left(6\cdot[1^*_7]_{n+1}\right)/6\]
Links
> 10004: Quasi Repdigit 100..004
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> 10006: Quasi Repdigit 100..006
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> 10111: Near Repdigit 1011..11
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> 11101: Near Repdigit 11..1101
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> 11111: Repunit 11..11
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> 11112: Near Repdigit 11..112
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> 11113: Near Repdigit 11..113
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> 11114: Near Repdigit 11..114
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> 11115: Near Repdigit 11..115
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> 11116: Near Repdigit 11..116
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> 11121: Near Repdigit 11..1121
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> 11131: Near Repdigit 11..1131
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> 11141: Near Repdigit 11..1141
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> 11151: Near Repdigit 11..1151
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> 11161: Near Repdigit 11..1161
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> 11311: Near Repdigit Palindrome 11..11311..11
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> 11411: Near Repdigit Palindrome 11..11411..11
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> 11511: Near Repdigit Palindrome 11..11511..11
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> 11611: Near Repdigit Palindrome 11..11611..11
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> 12111: Near Repdigit 1211..11
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> 12222: Near Repdigit 122..22
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> 12224: Quasi Repdigit 122..224
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> 12226: Quasi Repdigit 122..226
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> 13111: Near Repdigit 1311..11
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> 13331: Plateau 133..331
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> 13333: Near Repdigit 133..33
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> 13334: Quasi Repdigit 133..334
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> 13336: Quasi Repdigit 133..336
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> 14111: Near Repdigit 1411..11
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> 14442: Quasi Repdigit 144..442
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> 14444: Near Repdigit 144..44
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> 14446: Quasi Repdigit 144..446
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> 15111: Near Repdigit 1511..11
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> 15551: Plateau 155..551
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> 15552: Quasi Repdigit 155..552
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> 15553: Quasi Repdigit 155..553
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> 15555: Near Repdigit 155..55
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> 15556: Quasi Repdigit 155..556
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> 16111: Near Repdigit 1611..11
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> 16664: Quasi Repdigit 166..664
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> 16666: Near Repdigit 166..66
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