11111: Repunit 11..11

First few terms (base 10): \[[1^*_6]_n=\{0,1,7,43,259,\ldots\}\]

First few terms (base 6): \[\{\text{},\text{1},\text{11},\text{111},\text{1111},\ldots\}\]

General Formula:\[[1^*_6]_n={6^{n}-1\over5}\]

Equivalent Patterns: \[[5^*_6]_n=5\cdot[1^*_6]_n\] \[[45^*1_6]_n=25\cdot[1^*_6]_{n+1}\] \[[12^*1_6]_n=7\cdot[1^*_6]_{n+1}\] \[[23^*1_6]_n=13\cdot[1^*_6]_{n+1}\] \[[34^*1_6]_n=19\cdot[1^*_6]_{n+1}\] \[[2^*_6]_n=2\cdot[1^*_6]_n\] \[[15^*4_6]_n=10\cdot[1^*_6]_{n+1}\] \[[3^*_6]_n=3\cdot[1^*_6]_n\] \[[25^*3_6]_n=15\cdot[1^*_6]_{n+1}\] \[[4^*_6]_n=4\cdot[1^*_6]_n\] \[[35^*2_6]_n=20\cdot[1^*_6]_{n+1}\] \[[13^*2_6]_n=8\cdot[1^*_6]_{n+1}\] \[[14^*3_6]_n=9\cdot[1^*_6]_{n+1}\] \[[24^*2_6]_n=14\cdot[1^*_6]_{n+1}\]

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