22223: Near Repdigit 22..223

First few terms (base 10): \[[2^*3_5]_n=\{3,13,63,313,1563,\ldots\}\]

First few terms (base 5): \[\{\text{3},\text{23},\text{223},\text{2223},\text{22223},\ldots\}\]

General Formula:\[[2^*3_5]_n={5\cdot5^{n}+1\over2}\]

Equivalent Patterns: \[[10^*1_5]_n=2\cdot[2^*3_5]_n\] \[[20^*2_5]_n=4\cdot[2^*3_5]_n\] \[[12^*4_5]_n=3\cdot[2^*3_5]_n\] \[[30^*3_5]_n=6\cdot[2^*3_5]_n\] \[[40^*4_5]_n=8\cdot[2^*3_5]_n\]

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