10001: Depression 100..001

First few terms (base 10): \[[10^*1_6]_n=\{7,37,217,1297,7777,\ldots\}\]

First few terms (base 6): \[\{\text{11},\text{101},\text{1001},\text{10001},\text{100001},\ldots\}\]

General Formula:\[[10^*1_6]_n=6\cdot6^{n}+1\]

Equivalent Patterns: \[[50^*5_6]_n=5\cdot[10^*1_6]_n\] \[[20^*2_6]_n=2\cdot[10^*1_6]_n\] \[[30^*3_6]_n=3\cdot[10^*1_6]_n\] \[[40^*4_6]_n=4\cdot[10^*1_6]_n\]

Table

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