How is 12471116 a pattern?

That number as a whole is not a pattern, but when broken up into the following string of numbers, it is: 1, 2, 4, 7, 11, 16 We can test for several types of patterns if we look for what numbers can be added or subtracted at each step to result in the next number. The string above can be obtained by the following sequential additions: 0, +1, +2, +3, +4, +5 So, each number is the sum of the last number, and an incrementing digit. This makes it a series which can be defined in series notation as: a(n) = a(n-1) + n where n begins at zero. That means that any given number is equal to the previous number, plus it's position in the list. Therefore, the next number, which will be the seventh number in the list (n = 6), will be equal to 16 + 6, which is 22.