Fibonacci Number

It has a definition that the first 2 numbers in the sequence are 0 and 1.

F(p) = F(p-1) + F(p-2)

Here is the sequence for the first 25: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368 and 75025

It closely related to Pascal's Triangle


It also has a negative scale called the Negafibonacci Numbers.

F(-p) = (F(p))(-1)^(p+1)

It has the same scale except when p is even, F(-p) numbers are negative.

It is also involved with the Wall-Sun-Sun prime.

The equation used is F(p-(p/5)) and that p > 5, where the resulting number has to be prime and in integer form.

p = 10   F(10-(10/5)) = F(10-2) = F(8) = 21 (not prime)

It is believed that there are infinitely many Wall-Sun-Sun primes but yet there are none discovered to date.