33334: Near Repdigit 33..334

First few terms (base 10): \[[3^*4_7]_n=\{4,25,172,1201,8404,\ldots\}\]

First few terms (base 7): \[\{\text{4},\text{34},\text{334},\text{3334},\text{33334},\ldots\}\]

General Formula:\[[3^*4_7]_n={7\cdot7^{n}+1\over2}\]

Equivalent Patterns: \[[10^*1_7]_n=2\cdot[3^*4_7]_n\] \[[20^*2_7]_n=4\cdot[3^*4_7]_n\] \[[13^*5_7]_n=3\cdot[3^*4_7]_n\] \[[30^*3_7]_n=6\cdot[3^*4_7]_n\] \[[40^*4_7]_n=8\cdot[3^*4_7]_n\] \[[23^*6_7]_n=5\cdot[3^*4_7]_n\] \[[50^*5_7]_n=10\cdot[3^*4_7]_n\] \[[60^*6_7]_n=12\cdot[3^*4_7]_n\]

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