22223: Near Repdigit 22..223

First few terms (base 10): \[[2^*3_4]_n=\{3,11,43,171,683,\ldots\}\]

First few terms (base 4): \[\{\text{3},\text{23},\text{223},\text{2223},\text{22223},\ldots\}\]

General Formula:\[[2^*3_4]_n={8\cdot4^{n}+1\over3}\]

Equivalent Patterns: \[[20^*1_4]_n=3\cdot[2^*3_4]_n\] \[[31^*3_4]_n=5\cdot[2^*3_4]_n\] \[[1^*2_4]_n=2\cdot[2^*3_4]_{n-1}\] \[[10^*2_4]_n=6\cdot[2^*3_4]_{n-1}\]

Table

No table data.