number theory - Prove that there are arbitrarily long sequences of consecutive integers, none of which can be written as the sum of two perfect squares.

Prove that there are arbitrarily long sequences of consecutive integers, none of which can be written as the sum of two perfect squares.

First few numbers are $3,6,7,11,12,14,15,19,21,22,23,24,27,28,30,31,33,35,38,39, \cdots$

Sums of squares can only be of the form $4k$, $4k+1$ and $4k+2$. So can we use this idea to prove the proposition?

I didn't find a logical sequence. Can anyone provide some hints to proceed with this?