11112: Near Repdigit 11..112

First few terms (base 10): \[[1^*2_7]_n=\{2,9,58,401,2802,\ldots\}\]

First few terms (base 7): \[\{\text{2},\text{12},\text{112},\text{1112},\text{11112},\ldots\}\]

General Formula:\[[1^*2_7]_n={7\cdot7^{n}+5\over6}\]

Equivalent Patterns: \[[2^*4_7]_n=2\cdot[1^*2_7]_n\] \[[3^*6_7]_n=3\cdot[1^*2_7]_n\] \[[10^*5_7]_n=6\cdot[1^*2_7]_n\]

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