Formula explorer
Type any whole number and follow the seven steps that take it to an area, a residue and a musical interval. At the Lucas numbers the area is always a perfect square: the square of the matching Fibonacci number.
Lucas numbers:
The seven steps
Result
Around n
One full period of 25 around n; the pattern repeats every 25 and reads the same backwards around every multiple of 25.
Which areas are perfect squares?
Proved in the paper: for n ≥ 1, P(n) is a perfect square exactly when n is a Lucas number.