Problem 230Published on Saturday, 31st January 2009, 01:00 pm; Solved by 2022; Difficulty rating: 50%
For any two strings of digits, A and B, we define FA,B to be the sequence (A,B,AB,BAB,ABBAB,...) in which each term is the concatenation of the previous two.
Further, we define DA,B(n) to be the nth digit in the first term of FA,B that contains at least n digits.
Let A=1415926535, B=8979323846. We wish to find DA,B(35), say.
The first few terms of FA,B are:
Then DA,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:
and for B the next hundred digits:
Find ∑n = 0,1,...,17 10n× DA,B((127+19n)×7n) .