1,11,21,2111,111221,?,?
what are the next two numbers of this sequence?
Looks to me like you have a typo. I get
1,11,21,1211,111221,312211,13112221,...
or even
1,11,21,1211,3112,211213,312213,...
To find the next two numbers of the given sequence, we need to observe the pattern and try to understand the rule behind it.
Looking closely at the numbers in the sequence, we can see that each term describes the count or arrangement of digits in the previous term.
Let's break down the sequence step by step:
1. The first term is "1", which is a single digit. So, the count or arrangement of digits in the first term is "1".
2. The second term begins with a count or arrangement of characters in the previous term, which is "1". So, the second term is "11".
3. The third term is "21", which means there are 2 elements of the previous term (which is "11") and 1 element of the previous term (which is "1"). Therefore, the count or arrangement of characters in the third term is "21".
4. The fourth term is "2111", indicating that there are 1 element of the previous term (which is "21") and 1 element of the previous term (which is "1"). So, the count or arrangement of characters in the fourth term is "2111".
5. The fifth term is "111221", which suggests there are 3 elements of the previous term (which is "2111") and 2 elements of the previous term (which is "1"). Thus, the count or arrangement of characters in the fifth term is "111221".
Based on this pattern, we can infer the following steps:
6. The sixth term: Since the fifth term is "111221", we count: three 1's, two 2's, and one 1. So, the sixth term is "312211".
7. The seventh term: Since the sixth term is "312211", we count: one 3, one 2, and two 1's. Therefore, the seventh term is "13112221".
Hence, the next two numbers in the sequence are "312211" and "13112221".