Project Euler - Problem 230: Fibonacci Words

I wrote a Python script to solve Problem 230 on Project Euler. You can read the problem via the link. It involves a sequence known as Fibonacci Word. The sequences goes as follows:

A B AB BAB ABBAB BABABBAB ...

The above sequence of words is Fibonacci in that the length of the words form the sequence 1, 1, 2, 3, 5, 8, ...

My solution uses the Golden Ratio as a way to figure out whether we are in the A or B. The relationship between Fibonacci sequence and Gold Ratio is pretty well known.

g = 1.6180339887498949 # golden ratio

t = (
    '14159265358979323846264338327950288419716939937510' +
    '58209749445923078164062862089986280348253421170679',
    '82148086513282306647093844609550582231725359408128' +
    '48111745028410270193852110555964462294895493038196'
)

l = len(t[0])

def D(n):
    i = (n-1) % l
    j =  (n-1) // l
    k = 1 if j-1 <= j//g * g < j else 0 # magic
    return int(t[k][i])

print sum([10**i * D((127 + 19*i) * 7**i) for i in range(18)])

Another good read about this topic is the L-system, and also the Fibonacci Rectangle.