Answer:
The next two numbers following:
431
141311
1114111321
311431131211
are:
132114132113111221
AND
11131221141113122113312211
Step-by-step explanation:
I shall explain the pattern below:
431 (just the digits 4, 3, and 1)
141311 (one 4 becomes 14, one 3 becomes 13, one 1 becomes 11 -> looking at each digit of the previous number, 431)
1114111321 (one 1 becomes 11, one 4 becomes 14, one 1 becomes 11, one three becomes 13, two consecutive 1s becomes 21 -> looking at each digit of the previous number, 141311)
311431131211 (three consecutive 1s becomes 31, one 4 becomes 14, 3 more consecutive 1s becomes 31, one 3 becomes 13, one 2 becomes 12, and one 1 becomes 11 -> looking at each digit of the previous number, 1114111321)
NEXT TWO NUMBERS:
one 3 (13), two consecutive 1s (21), one 4 (14), one 3 (13), two consecutive 1s (21), one 3 (13), one 1 (11), one 2 (12), two consecutive 1s (21)
that makes: 132114132113111221
one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 4 (14), one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 3 (13), three consecutive 1s (31), two consecutive 2s (22), one 1 (11)
that makes: 11131221141113122113312211
The rule is that the next number is essentially the previous number with the number of times each digit appears consecutively before each digit of the previous number. I know that sounds convoluted. Hopefully it makes enough sense. Let me know if I should explain more fully.
