11112: Near Repdigit 11..112

First few terms (base 10): \[[1^*2_{10}]_n=\{2,12,112,1112,11112,\ldots\}\]

General Formula:\[[1^*2_{10}]_n=2\cdot{5\cdot10^{n}+4\over9}\]

Equivalent Patterns: \[[5^*6_{10}]_n=[1^*2_{10}]_{n+1}/2\] \[[27^*8_{10}]_n=[1^*2_{10}]_{n+2}/4\] \[[3^*6_{10}]_n=3\cdot[1^*2_{10}]_n\] \[[16^*8_{10}]_n=3\cdot[1^*2_{10}]_{n+1}/2\] \[[83^*4_{10}]_n=3\cdot[1^*2_{10}]_{n+2}/4\] \[[10^*8_{10}]_n=9\cdot[1^*2_{10}]_n\] \[[50^*4_{10}]_n=9\cdot[1^*2_{10}]_{n+1}/2\] \[[2^*4_{10}]_n=2\cdot[1^*2_{10}]_n\] \[[4^*8_{10}]_n=4\cdot[1^*2_{10}]_n\] \[[61^*6_{10}]_n=11\cdot[1^*2_{10}]_{n+1}/2\] \[[72^*8_{10}]_n=13\cdot[1^*2_{10}]_{n+1}/2\]

See Also: Factorization of 100..008 on stdkmd.net

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