Project Euler/230

Problem Statement

Fibonacci Words

For any two strings of digits, A and B, we define F_{A,B} to be the sequence (A, B, AB, BAB, ABBAB, ...) in which each term is the concatenation of the previous two.

Further, we define D_{A,B}(n) to be the nth digit in the first term of F_{A,B} that contains at least n digits.

Example: Let A=1415926535, B=8979323846. We wish to find D_{A,B}(35), say. The first few terms of F_{A,B} are: 1415926535 8979323846 14159265358979323846 897932384614159265358979323846 14159265358979323846897932384614159265358979323846

Then D_{A,B}(35) is the 35th digit in the fifth term, which is 9.

Now we use for A the first 100 digits of π behind the decimal point: 14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679

and for B the next hundred digits: 82148086513282306647093844609550582231725359408128 48111745028410270193852110555964462294895493038196 .

Find ∑_{n = 0,1,...,17} 10^n × D_{A,B}((127+19n)×7^n).