Concordant sequences and concordant entire functions

A theorem of Pólya shows that the function 2 ^Z is the ‘smallest’ transcendental entire function that is integer valued on the set ℕ of non-negative integers. Analogous results have been established in which ℕ is replaced by other sets of integers, beginning with the result of Gel’fond for geometric sequences of integers. Other results consider the imposition of additional congruence conditions on the value sequence of the candidate entire function on the subject sequence. The present paper extends the consideration of such congruence conditions from ℕ and geometric sequences to more general sets for which Pólya-type results have been established.