10111: Near Repdigit 1011..11

First few terms (base 10): \[[101^*_7]_n=\{7,50,351,2458,17207,\ldots\}\]

First few terms (base 7): \[\{\text{10},\text{101},\text{1011},\text{10111},\text{101111},\ldots\}\]

General Formula:\[[101^*_7]_n={43\cdot7^{n}-1\over6}\]

Equivalent Patterns: \[[202^*_7]_n=2\cdot[101^*_7]_n\] \[[303^*_7]_n=3\cdot[101^*_7]_n\] \[[606^*_7]_n=6\cdot[101^*_7]_n\] \[[404^*_7]_n=4\cdot[101^*_7]_n\] \[[505^*_7]_n=5\cdot[101^*_7]_n\]

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