11111: Repunit 11..11

First few terms (base 10): \[[1^*_3]_n=\{0,1,4,13,40,\ldots\}\]

First few terms (base 3): \[\{\text{},\text{1},\text{11},\text{111},\text{1111},\ldots\}\]

General Formula:\[[1^*_3]_n={3^{n}-1\over2}\]

Equivalent Patterns: \[[2^*_3]_n=2\cdot[1^*_3]_n\] \[[12^*1_3]_n=4\cdot[1^*_3]_{n+1}\]

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