560 is in the sequence because in base 3 it is 202202, in base 4 it is 20300 and in base 5 it is 4220.
MAPLE
a:=proc(n) if member(1, convert(convert(n, base, 3), set) union convert(convert(n, base, 4), set) union convert(convert(n, base, 5), set))=false then n else fi end: seq(a(n), n=0..170000); # Emeric Deutsch, Apr 30 2006
MATHEMATICA
Select[Range[0, 200000], Table[DigitCount[#, n, 1], {n, 3, 5}]=={0, 0, 0}&] (* Harvey P. Dale, Jan 17 2014 *)