For any three consecutive members of a sequence, the first and third members are near consecutive.
1 squared is 1. 2 squared is 4. So 1 and 4 are consecutive perfect squares.
1 squared is 1. 3 squared is 9. So 1 and 9 are near consecutive perfect squares.
I want to verify this formula to go from any perfect square to the next near consecutive perfect square. Let a be any perfect square. Let c be the next near consecutive perfect square. Here is the formula:
a+4(1+$\sqrt a$)=c
Example:
49+4(1+$\sqrt 49$)=81
Did I get the formula right? Is my terminology ok?
Best Answer
Yes! Its right! If your square is $a$ then the number that originate it is $\sqrt{a}$ thus the next near consecutive perfect square is $(\sqrt{a}+2)^2$, but $(\sqrt{a}+2)^2 = a + 4(\sqrt{a}+1)$