44445: Near Repdigit 44..445

First few terms (base 10): \[[4^*5_9]_n=\{5,41,365,3281,29525,\ldots\}\]

First few terms (base 9): \[\{\text{5},\text{45},\text{445},\text{4445},\text{44445},\ldots\}\]

General Formula:\[[4^*5_9]_n={9\cdot9^{n}+1\over2}\]

Equivalent Patterns: \[[10^*1_9]_n=2\cdot[4^*5_9]_n\] \[[20^*2_9]_n=4\cdot[4^*5_9]_n\] \[[40^*4_9]_n=8\cdot[4^*5_9]_n\] \[[24^*7_9]_n=5\cdot[4^*5_9]_n\] \[[50^*5_9]_n=10\cdot[4^*5_9]_n\] \[[34^*8_9]_n=7\cdot[4^*5_9]_n\] \[[70^*7_9]_n=14\cdot[4^*5_9]_n\] \[[80^*8_9]_n=16\cdot[4^*5_9]_n\] \[[14^*6_9]_n=3\cdot[4^*5_9]_n\] \[[30^*3_9]_n=6\cdot[4^*5_9]_n\] \[[60^*6_9]_n=12\cdot[4^*5_9]_n\]

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