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COMMENTS
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Since A010888(a(n)) = 9 the sequence is free of primes. For squares see A065752. Replacing "0" by "(", "9" by ")", "1" by "[", "8" by "]", "2" by "{", "7" by "}", "3" by "<", "6" by ">", "4" by "d" and "5" by "b" yields well formed bracket expressions - but not the full Dyck-language, as the defining grammar is not generating words with leading zeros.
For example [], {}, <>, db, [()], [[]], [{}], [<>], [db], [](), [][], []{}, []<>, []db, {()}, {[]}, {{}}, {<>}, {db}, {}(), {}[], {}{}, {}<>, {}db, <()>, <[]>, <{}>, <<>>, <db>, <>(), <>[], <>{}, <><>, <>db, d()b, d[]b, d{}b, d<>b, ddbb, db(), db[], db{}, db<>, dbdb, [(())], [([])], [({})], [(<>)], [(db)], [()()], [()[]], [(){}], [()<>], [()db], [()](), [()][], [()]{}, [()]<>, [()]db, [[()]], [[[]]], [[{}]], [[<>]], [[db]], [[]()], [[][]], [[]{}], [[]<>], [[]db], [[]](), [[]][], [[]]{}, [[]]<>, [[]]db, [{()}], [{[]}], [{{}}], [{<>}], [{db}], [{}()].
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