This week in Thinking Thursday I asked you to find the next number in the sequence:
Who discovered that it is 311 311 222 113?
If you did, then well done!
So how do you get there?
Well this is what’s known as a look-and-say sequence in which each term is constructed by describing the previous term.
So if we start with the number 3, the next term is “one 3” as the previous number contains just one of the number three. So now we have 3, 13.
And the third number describes the second number, hence it is “one 1, one 3” or 1113, which we wrote as 1 113 just to throw you off the scent a bit. We now have 3, 13, 1 113.
Similarly, number four is constructed from number three: “three 1s, one 3”; or 3 113, giving us the sequence 3, 13, 1 113, 3 113. And so on.
But do you notice something else about this sequence? Yes, that’s right, the last number is always 3. In fact that’s true for any look-and-say sequence which starts with an integer between 0 and 9 — the last digit of each term will always be the starting number.
What I didn’t know was that the look-and-say sequence was introduced and analysed by the British mathematician John Conway who is still alive, and who also invented the Game of Life.
Good fun!