When modular arithmetic is applied to it, (*) Pisano periods can be observed.
The fact that the n-th element of this is divisible by the square of the i-th element of this if and only if n is divisible by the i-th element of this gave a solution to the Julia Robinson Hypothesis. The divisibility properties of this allowed the proof that recursively enumerable sets are equivalent to Diophantine sets by Yuri Matiyasevich and thus solve Hilbert's tenth problem. When modular arithmetic is applied to it, (*) Pisano periods can be observed. Its closed-form solution is known as Binet's formula, and it was introduced in the West in the book Liber Abaci. The numbers comprising this sequence, which is a type of Lucas sequence, are the sums of successive "shallow" diagonals of Pascal's Triangle. Originally devised to study the growth of an hypothetical rabbit population, for 10 points, name this sequence, beginning 0, 1, 1, 2, 3, 5, in which each term is the sum of the two before it.
The fact that the n-th element of this is divisible by the square of the i-th element of this if and only if n is divisible by the i-th element of this gave a solution to the Julia Robinson Hypothesis.
Fibonacci sequence