Digital Sum

\(Let\quad { a }_{ 1 }={ 9999 }^{ { 8888 }^{ { 7777... }^{ ..1111 } } }+{ 3333 }^{ { 2222 }^{ 1111 } }\\ Let\quad { a }_{ n+1 }\quad be\quad the\quad digital\quad sum\quad of\quad { a }_{ n }\quad in\quad base\quad 10.\\ Find\quad { a }_{ { a }_{ 1 } }.\)

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