44445: Near Repdigit 44..445

First few terms (base 10): \[[4^*5_6]_n=\{5,29,173,1037,6221,\ldots\}\]

First few terms (base 6): \[\{\text{5},\text{45},\text{445},\text{4445},\text{44445},\ldots\}\]

General Formula:\[[4^*5_6]_n={24\cdot6^{n}+1\over5}\]

Equivalent Patterns: \[[40^*1_6]_n=5\cdot[4^*5_6]_n\] \[[53^*5_6]_n=7\cdot[4^*5_6]_n\] \[[13^*4_6]_n=2\cdot[4^*5_6]_n\] \[[1^*3_6]_n=9\cdot[4^*5_6]_{n-2}\] \[[2^*3_6]_n=3\cdot[4^*5_6]_{n-1}\] \[[20^*3_6]_n=15\cdot[4^*5_6]_{n-1}\] \[[31^*2_6]_n=4\cdot[4^*5_6]_n\] \[[3^*43_6]_n=27\cdot[4^*5_6]_{n-1}\]

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