11111: Repunit 11..11

First few terms (base 10): \[[1^*_5]_n=\{0,1,6,31,156,\ldots\}\]

First few terms (base 5): \[\{\text{},\text{1},\text{11},\text{111},\text{1111},\ldots\}\]

General Formula:\[[1^*_5]_n={5^{n}-1\over4}\]

Equivalent Patterns: \[[2^*_5]_n=2\cdot[1^*_5]_n\] \[[4^*_5]_n=4\cdot[1^*_5]_n\] \[[14^*3_5]_n=8\cdot[1^*_5]_{n+1}\] \[[3^*_5]_n=3\cdot[1^*_5]_n\] \[[12^*1_5]_n=6\cdot[1^*_5]_{n+1}\] \[[24^*2_5]_n=12\cdot[1^*_5]_{n+1}\] \[[34^*1_5]_n=16\cdot[1^*_5]_{n+1}\] \[[13^*2_5]_n=7\cdot[1^*_5]_{n+1}\] \[[23^*1_5]_n=11\cdot[1^*_5]_{n+1}\]

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