44445: Near Repdigit 44..445

First few terms (base 10): \[[4^*5_7]_n=\{5,33,229,1601,11205,\ldots\}\]

First few terms (base 7): \[\{\text{5},\text{45},\text{445},\text{4445},\text{44445},\ldots\}\]

General Formula:\[[4^*5_7]_n={14\cdot7^{n}+1\over3}\]

Equivalent Patterns: \[[20^*1_7]_n=3\cdot[4^*5_7]_n\] \[[12^*3_7]_n=2\cdot[4^*5_7]_n\] \[[40^*2_7]_n=6\cdot[4^*5_7]_n\] \[[60^*3_7]_n=9\cdot[4^*5_7]_n\] \[[24^*6_7]_n=4\cdot[4^*5_7]_n\] \[[32^*4_7]_n=5\cdot[4^*5_7]_n\] \[[52^*5_7]_n=8\cdot[4^*5_7]_n\]

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