Deterministic primality test for numbers of the form $A^2.3^n+1$, $n \ge 3$ odd

We use a result of E. Lehmer in cubic residuacity to find an algorithm to determine primality of numbers of the form $A^23^n+1$, $n$ odd, $A^2<4(3^n+1)$. The algorithm represents an improvement over the more general algorithm that determines primality of numbers of the form $A.3^n \pm 1$, $A/2<4.3^n-1$, presented by Berrizbeitia and Berry (1999).