11111: Repunit 11..11
First few terms (base 10): \[[1^*_{10}]_n=\{0,1,11,111,1111,\ldots\}\]
General Formula:\[[1^*_{10}]_n={10^{n}-1\over9}\]
Equivalent Patterns: \[[3^*_{10}]_n=3\cdot[1^*_{10}]_n\] \[[9^*_{10}]_n=9\cdot[1^*_{10}]_n\] \[[29^*7_{10}]_n=27\cdot[1^*_{10}]_{n+1}\] \[[7^*_{10}]_n=7\cdot[1^*_{10}]_n\] \[[23^*1_{10}]_n=21\cdot[1^*_{10}]_{n+1}\] \[[69^*3_{10}]_n=63\cdot[1^*_{10}]_{n+1}\] \[[89^*1_{10}]_n=81\cdot[1^*_{10}]_{n+1}\] \[[12^*1_{10}]_n=11\cdot[1^*_{10}]_{n+1}\] \[[36^*3_{10}]_n=33\cdot[1^*_{10}]_{n+1}\] \[[14^*3_{10}]_n=13\cdot[1^*_{10}]_{n+1}\] \[[18^*7_{10}]_n=17\cdot[1^*_{10}]_{n+1}\] \[[56^*1_{10}]_n=51\cdot[1^*_{10}]_{n+1}\] \[[25^*3_{10}]_n=23\cdot[1^*_{10}]_{n+1}\] \[[34^*1_{10}]_n=31\cdot[1^*_{10}]_{n+1}\] \[[45^*1_{10}]_n=41\cdot[1^*_{10}]_{n+1}\] \[[47^*3_{10}]_n=43\cdot[1^*_{10}]_{n+1}\] \[[58^*3_{10}]_n=53\cdot[1^*_{10}]_{n+1}\] \[[67^*1_{10}]_n=61\cdot[1^*_{10}]_{n+1}\] \[[78^*1_{10}]_n=71\cdot[1^*_{10}]_{n+1}\] \[[2^*_{10}]_n=2\cdot[1^*_{10}]_n\] \[[6^*_{10}]_n=6\cdot[1^*_{10}]_n\] \[[19^*8_{10}]_n=18\cdot[1^*_{10}]_{n+1}\] \[[4^*_{10}]_n=4\cdot[1^*_{10}]_n\] \[[13^*2_{10}]_n=12\cdot[1^*_{10}]_{n+1}\] \[[39^*6_{10}]_n=36\cdot[1^*_{10}]_{n+1}\] \[[5^*_{10}]_n=5\cdot[1^*_{10}]_n\] \[[16^*5_{10}]_n=15\cdot[1^*_{10}]_{n+1}\] \[[49^*5_{10}]_n=45\cdot[1^*_{10}]_{n+1}\] \[[59^*4_{10}]_n=54\cdot[1^*_{10}]_{n+1}\] \[[8^*_{10}]_n=8\cdot[1^*_{10}]_n\] \[[26^*4_{10}]_n=24\cdot[1^*_{10}]_{n+1}\] \[[79^*2_{10}]_n=72\cdot[1^*_{10}]_{n+1}\] \[[15^*4_{10}]_n=14\cdot[1^*_{10}]_{n+1}\] \[[46^*2_{10}]_n=42\cdot[1^*_{10}]_{n+1}\] \[[17^*6_{10}]_n=16\cdot[1^*_{10}]_{n+1}\] \[[24^*2_{10}]_n=22\cdot[1^*_{10}]_{n+1}\] \[[27^*5_{10}]_n=25\cdot[1^*_{10}]_{n+1}\] \[[28^*6_{10}]_n=26\cdot[1^*_{10}]_{n+1}\] \[[35^*2_{10}]_n=32\cdot[1^*_{10}]_{n+1}\] \[[37^*4_{10}]_n=34\cdot[1^*_{10}]_{n+1}\] \[[38^*5_{10}]_n=35\cdot[1^*_{10}]_{n+1}\] \[[48^*4_{10}]_n=44\cdot[1^*_{10}]_{n+1}\] \[[57^*2_{10}]_n=52\cdot[1^*_{10}]_{n+1}\] \[[68^*2_{10}]_n=62\cdot[1^*_{10}]_{n+1}\]
See Also: Factorization of 11..11 on stdkmd.net
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