11114: Near Repdigit 11..114

First few terms (base 10): \[[1^*4_9]_n=\{4,13,94,823,7384,\ldots\}\]

First few terms (base 9): \[\{\text{4},\text{14},\text{114},\text{1114},\text{11114},\ldots\}\]

General Formula:\[[1^*4_9]_n={9\cdot9^{n}+23\over8}\]

Equivalent Patterns: \[[2^*8_9]_n=2\cdot[1^*4_9]_n\] \[[3^*43_9]_n=3\cdot[1^*4_9]_{n+1}\] \[[6^*86_9]_n=6\cdot[1^*4_9]_{n+1}\]

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