0,1

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}], [{}()].

Grammar with auxiliaries s and x (s as axiom), decimal digits as terminal alphabet and 27 rules in BNF: s : := 18 | 27 | 36 | 45 | 1x8 | 2x7 | 3x6 | 4x5 | 18x | 27x | 36x | 45x | 1x8x | 2x7x | 3x6x | 4x5x x : := 09 | 18 | 27 | 36 | 45 | 0x9 | 1x8 | 2x7 | 3x6 | 4x5 | xx.

Parsing A065752(5) = 1274275809 <- 1x4275809 <- 1x4x5809 <- 1xx809 <- 1x809 <- 1x8x <- s.

Sequence in context: A090064 A082804 A109911 this_sequence A038632 A138336 A094224

Adjacent sequences: A065748 A065749 A065750 this_sequence A065752 A065753 A065754

base,nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 17 2001