44445: Near Repdigit 44..445

First few terms (base 10): \[[4^*5_8]_n=\{5,37,293,2341,18725,\ldots\}\]

First few terms (base 8): \[\{\text{5},\text{45},\text{445},\text{4445},\text{44445},\ldots\}\]

General Formula:\[[4^*5_8]_n={32\cdot8^{n}+3\over7}\]

Equivalent Patterns: \[[40^*3_8]_n=7\cdot[4^*5_8]_n\] \[[15^*7_8]_n=3\cdot[4^*5_8]_n\] \[[51^*5_8]_n=9\cdot[4^*5_8]_n\] \[[62^*7_8]_n=11\cdot[4^*5_8]_n\] \[[1^*2_8]_n=2\cdot[4^*5_8]_{n-1}\] \[[10^*6_8]_n=14\cdot[4^*5_8]_{n-1}\] \[[2^*4_8]_n=4\cdot[4^*5_8]_{n-1}\] \[[3^*6_8]_n=6\cdot[4^*5_8]_{n-1}\]

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