Look and say sequence
Problem 419Published on Saturday, 16th March 2013, 10:00 pm; Solved by 225
The look and say sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.
It helps to do this out loud:
1 is 'one one' 11
11 is 'two ones' 21
21 is 'one two and one one' 1211
1211 is 'one one, one two and two ones' 111221
111221 is 'three ones, two twos and one one' 312211
Define A(n), B(n) and C(n) as the number of ones, twos and threes in the n'th element of the sequence respectively.
One can verify that A(40) = 31254, B(40) = 20259 and C(40) = 11625.
Find A(n), B(n) and C(n) for n = 1012.
Give your answer modulo 230 and separate your values for A, B and C by a comma.
E.g. for n = 40 the answer would be 31254,20259,11625