11111: Repunit 11..11

First few terms (base 10): \[[1^*_7]_n=\{0,1,8,57,400,\ldots\}\]

First few terms (base 7): \[\{\text{},\text{1},\text{11},\text{111},\text{1111},\ldots\}\]

General Formula:\[[1^*_7]_n={7^{n}-1\over6}\]

Equivalent Patterns: \[[2^*_7]_n=2\cdot[1^*_7]_n\] \[[3^*_7]_n=3\cdot[1^*_7]_n\] \[[6^*_7]_n=6\cdot[1^*_7]_n\] \[[4^*_7]_n=4\cdot[1^*_7]_n\] \[[16^*5_7]_n=12\cdot[1^*_7]_{n+1}\] \[[13^*2_7]_n=9\cdot[1^*_7]_{n+1}\] \[[26^*4_7]_n=18\cdot[1^*_7]_{n+1}\] \[[12^*1_7]_n=8\cdot[1^*_7]_{n+1}\] \[[36^*3_7]_n=24\cdot[1^*_7]_{n+1}\] \[[5^*_7]_n=5\cdot[1^*_7]_n\] \[[14^*3_7]_n=10\cdot[1^*_7]_{n+1}\] \[[23^*1_7]_n=15\cdot[1^*_7]_{n+1}\] \[[46^*2_7]_n=30\cdot[1^*_7]_{n+1}\] \[[56^*1_7]_n=36\cdot[1^*_7]_{n+1}\] \[[24^*2_7]_n=16\cdot[1^*_7]_{n+1}\] \[[15^*4_7]_n=11\cdot[1^*_7]_{n+1}\] \[[34^*1_7]_n=22\cdot[1^*_7]_{n+1}\] \[[25^*3_7]_n=17\cdot[1^*_7]_{n+1}\] \[[35^*2_7]_n=23\cdot[1^*_7]_{n+1}\] \[[45^*1_7]_n=29\cdot[1^*_7]_{n+1}\]

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