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What’s next? 0, 4, 8, 21, 52, 65, 96, ? Question
What’s the next number in the following sequence:
0, 4, 8, 21, 52, 65, 96, ?
3 answers
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| will.octagon.gibson | (no comment) | Mar 3, 2026 at 04:14 |
Spoiler
The next number is 1.
The next number is derived from adding 4, then reversing the result.
0 -> 4 -> 4
4 -> 8 -> 8
8 -> 12 -> 21
21 -> 25 -> 52
52 -> 56 -> 65
65 -> 69 -> 96
96 -> 100 -> 1
This is very likely not what you had in mind, but mathematically there are always ways to find the "next" number in a sequence.
The simplest is finding the differences between numbers, then the difference between those differences, etc, until you get to all zeros or a single number. Once you get to a single number, you declare all higher differences to be 0. This is the same as saying you consider the original sequence the output of a polynomial resulting from fixed increases in X. The method uses the lowest-order polynomial to fit all the points, then extrapolates new values from there.
Analysis applied to your sequence:
0 4 8 21 52 65 96
4 4 13 31 13 31
0 9 18 -18 18
9 9 -36 36
0 -45 72
-45 117
162
In this case we had to go all the way to a single number since none of the rows was all-zero. Of course there are an infinite number of possible answers. We pick the one that is most "simple" by declaring all higher deltas to be 0. Applied to your sequence, to find the next number we start at the bottom and compute the next row on the right:
0 4 8 21 52 65 96 532
4 4 13 31 13 31 436
0 9 18 -18 18 405
9 9 -36 36 387
0 -45 72 351
-45 117 279
162 162
The answer therefore is 532. Note that we have actually created a continuous function that returns the input values exactly, but that allows us to find the value anywhere. There are an infinite number of functions that can do that, so we added the additional constraint that it be a polynomial with the minimum necessary order.
Again, I understand this is very unlikely what you had in mind. However, it is as valid as any solution given your under-constrained problem.
1 comment thread
Ok, I'm willing to embarrass myself with a probably-wrong answer, because I'm enjoying trying to figure it out. I see a pattern, but I can't explain the entire sequence using it, so I'm clearly missing something.
spoiler
The next number in the sequence is 109, and the one after that is 140.Starting with 21, the values alternate between +31 and +13. But I don't know what to do with 0, 4, 8.
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