  Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers .
We consider a specific sequence of differential operators Tk(n),{\lambda} ,
n=1,2,... on the space of entire functions , that depend on the sequence (k(n))
n=1,2,... and the non-zero complex number {\lambda} . We establish the
existence of an entire function f , such that for every positive number
{\lambda} the set {Tk(n),{\lambda} ,n=1,2,... } is dense in the space of entire
functions endowed with the topology of uniform convergence on compact subsets
of the complex plane . This provides the best possible strenghthened version of
a corresponding result due to Costakis and Sambarino [9] . From this and using
a non-trivial result of Weyl which concerns the uniform distribution modulo 1
of certain sequences and Cavalieri principle we can extend our result for a
subset of the set of complex numbers with full 2-dimentional Lebesque measure .
