0
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What's the next number?

8, 20, 40, 68, 104, 122, 170, 226, 290, 362, 442

EDIT (since we already have some answers below which assumed the next number correctly) ... For the record, here are some further numbers in the sequence:

530, 626, 730, 842, 962, 1090, 1226

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  • $\begingroup$ @Rubio The problem is that now I myself forgot how I constructed the sequence. $\endgroup$ – Vincent Mia Edie Verheyen Jun 23 '18 at 2:41
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    $\begingroup$ Well - that's not ideal, is it! The latest answer seems to be a complete solution, even if perhaps not your intended solution; if there's a reason it's not a fitting answer, I don't see it - is there a reason not to accept it? $\endgroup$ – Rubio Jun 23 '18 at 7:55
  • $\begingroup$ I meant shoover's. $\endgroup$ – Rubio Jun 23 '18 at 7:58
  • $\begingroup$ @Rubio I didn't check if that works out for all of the numbers stated. Did you? $\endgroup$ – Vincent Mia Edie Verheyen Jun 23 '18 at 8:02
  • $\begingroup$ Yes; it fits the original pattern and the hint exactly. $\endgroup$ – Rubio Jun 23 '18 at 8:04
2
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A generating expression for your sequence is

$(2x-\lfloor\log_{10}(2x-1)\rfloor)^2 + (2-\lfloor\log_{10}(2x-1)\rfloor)^2$ for $x\in\Bbb{Z^+}$

You've given the values for $x=1,\ldots,18$, which gives the next elements as

$1370, 1522, 1682, 1850, 2026, \ldots$

for $x=19,\ldots,23$ on up to

$9410, 9802, 10000, 10404, 10816, \ldots$

for $x=49,\ldots,53$ and beyond.

But that doesn't make for a very satisfying puzzle, so I suspect that's not the answer you're looking for.

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3
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Next number could be

530 (Which is square of 23 plus 1)

As,

the first 5 numbers were obtained by adding 4 to the squares of even numbers- 2,4,6,8 and 10.

Then,

1 is getting added to the squares of odd numbers - 11, 13, 15, 17, 19, 21. So the next number could be square of 23 that is 529 and 1 added to it.

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  • $\begingroup$ Not bad, but there is a more elegant way, which doesn't discriminate between the first five numbers and the remaining numbers. $\endgroup$ – Vincent Mia Edie Verheyen Jun 12 '18 at 0:12
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It looks like the answer is

530

Because

the difference increases by 8 each time

although that breaks down for

104, 122, 170 - so unless that's a mistake my answer is wrong

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