11111: Repunit 11..11

First few terms (base 10): \[[1^*_4]_n=\{0,1,5,21,85,\ldots\}\]

First few terms (base 4): \[\{\text{},\text{1},\text{11},\text{111},\text{1111},\ldots\}\]

General Formula:\[[1^*_4]_n={4^{n}-1\over3}\]

Equivalent Patterns: \[[3^*_4]_n=3\cdot[1^*_4]_n\] \[[23^*1_4]_n=9\cdot[1^*_4]_{n+1}\] \[[12^*1_4]_n=5\cdot[1^*_4]_{n+1}\] \[[2^*_4]_n=2\cdot[1^*_4]_n\] \[[13^*2_4]_n=6\cdot[1^*_4]_{n+1}\]

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