a(5)=9 since 9 is not equal to 2*a(k)+1 nor 3*a(k)+1 for 1<=k<5; and since 9 is allowed to be present, then 19(=2*9+1) and 28(=3*9+1) are to be excluded.
MATHEMATICA
s = {1}; Do[u = Union[s, 2s + 1, 3s + 1]; c = Complement[Range[u // Last], u] // First; AppendTo[s, c], {10000}]; s (* Jean-François Alcover, Dec 11 2012 *)
PROG
(Haskell)
import Data.List (delete)
a077477 n = a077477_list !! (n-1)
a077477_list = f [1..] where
f (x:xs) = x : f (delete (2*x + 1) $ delete (3*x + 1) xs)
