51111: Near Repdigit 511..11

First few terms (base 10): \[[51^*_8]_n=\{5,41,329,2633,21065,\ldots\}\]

First few terms (base 8): \[\{\text{5},\text{51},\text{511},\text{5111},\text{51111},\ldots\}\]

General Formula:\[[51^*_8]_n={36\cdot8^{n}-1\over7}\]

Equivalent Patterns: \[[12^*_8]_n=2\cdot[51^*_8]_{n-1}\] \[[24^*_8]_n=4\cdot[51^*_8]_{n-1}\] \[[36^*_8]_n=6\cdot[51^*_8]_{n-1}\] \[[63^*2_8]_n=10\cdot[51^*_8]_n\] \[[75^*4_8]_n=12\cdot[51^*_8]_n\]

Table

No table data.