The characteristic sequence of the integers that are the sum of two squares is not morphic

Let ( s 2 ( n ) ) n ∈ N be a 0 , 1 -sequence such that, for any natural number n , s 2 ( n ) = 1 if and only if n is a sum of two squares. In a recent article, Tahay proved that the sequence ( s 2 ( n ) ) n ∈ N is not k -automatic for any integer k , and asked if this sequence can be morphic. In this note, we give a negative answer to this question.