# Give the square that satisfy given equation? An=3n+1 of at least 5 terms

Not sure what you are asking for here but the following are squares within the given series ${A}_{n} = 3 n + 1$:
color(white)("XXX")color(blue)({A_0=1^2,A_1=2^2,A_5=4^2,A_8=5^2,A_16=7^2,A_21=8^2,...}
If this is what you are asking for, probably the easiest way to get the result is to list integer squares and check if, after division by $3$, there is a remainder of $1$