Source code in the jq programming language

def A000037: . + (0.5 + sqrt | floor);

def is_square: sqrt | . == floor;

"For n up to and including 22:",
 (range(1;23) | A000037),
"Check for squares for n up to 1e6:",
 (range(1;1e6+1) | A000037 | select( is_square ))

$ jq -n -r -f sequence_of_non-squares.jq
For n up to and including 22:
2
3
5
6
7
8
10
11
12
13
14
15
17
18
19
20
21
22
23
24
26
27
Check for squares for n up to 1e6:
$