22223: Near Repdigit 22..223

First few terms (base 10): \[[2^*3_7]_n=\{3,17,115,801,5603,\ldots\}\]

First few terms (base 7): \[\{\text{3},\text{23},\text{223},\text{2223},\text{22223},\ldots\}\]

General Formula:\[[2^*3_7]_n={7\cdot7^{n}+2\over3}\]

Equivalent Patterns: \[[10^*2_7]_n=3\cdot[2^*3_7]_n\] \[[4^*6_7]_n=2\cdot[2^*3_7]_n\] \[[20^*4_7]_n=6\cdot[2^*3_7]_n\] \[[30^*6_7]_n=9\cdot[2^*3_7]_n\] \[[12^*5_7]_n=4\cdot[2^*3_7]_n\]

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