Motivated with this question I formulated following question :

Does $\lfloor \sqrt{p} \rfloor$ generate all natural numbers where $p$ is a prime number of the form $4k+3$ ?

I wrote Maxima implementation of this generator :

```
P:[];
N:[];
p:3;
while p<20000 do
(if (mod(p,4)=3) then P:append(P,[p]),
p:next_prime(p))$
for i from 1 thru length(P) do
(m:floor(sqrt(P[i])),
if (not member(m,N)) then N:append(N,[m]))$
N;
```

You can run this code here .