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What's the next number in the following sequence:

1, 3, 6, 7, 9, 11, 13, 14, 18, 21, 23, 28, 31, ___, ...

Not sure if this one is easy. Hints will be released gradually. First one is in the title :)

Hint #2

Depending on where you live, you may have never seen these numbers.

Additionally

Never seeing these numbers is in fact an advantage, not disadvantage.

Hint #3

No math involved (except for counting)

Hint #4

Human brain may not be enough. Ask Google or Wikipedia for help.

Final Hint

How do you search for a sequence in Google that you've never seen, or even has never existed? Google is not that powerful to find something nonexistent for you. You need to search for something else.

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  • $\begingroup$ From Hint 2: Does this mean that someone in a different geographical location to you would be unable to solve this 'with ease'? $\endgroup$ – Inazuma Jun 9 '16 at 20:25
  • $\begingroup$ No, I believe it shouldn't matter. You may need the same kind of "help" anyway. $\endgroup$ – user24855 Jun 9 '16 at 20:27
  • $\begingroup$ Maybe a hint?.. $\endgroup$ – nicael Jun 10 '16 at 10:25
  • $\begingroup$ @nicael updated :) $\endgroup$ – user24855 Jun 10 '16 at 12:01
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Answer is:

32

Search google for the remaining numbers in the sequence:

https://goo.gl/oTOCNA

Which gives

The labels of Interstate higways. With both sequences one gets 1,2,3,4,5,6,7,8...

Image added:

enter image description here

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$32$.

Why?

When put into a $2$ by $n$ field, a pattern is formed. It's shown in the green section. The red parts are the next sections of the sequence. Black spots are numbers in the sequence. This is read as $1$ at the top, $2$ at the bottom, $3$ on the top and one to the right and so on. enter image description here

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    $\begingroup$ Hmm, I don't quite get it... :P This doesn't seem to work well with the hints. $\endgroup$ – user24855 Jun 9 '16 at 17:20
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Well, I realize it could be weird, but still -

$33$

The assumptions are

Every ten numbers begin with ones which have $1$ and $3$ as the last digit, the further numbers differ
$1,3,6,7,9$
$1,3,4,8$
$1,3,8$
$1,?$ Hence, it would look that the next number should end with $3$

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  • $\begingroup$ It's not that complicated :) $\endgroup$ – user24855 Jun 9 '16 at 15:30
  • $\begingroup$ @Pig You mean what, the rule is way easier? $\endgroup$ – nicael Jun 9 '16 at 15:58
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    $\begingroup$ It does not involve any complicated mathematical analysis. $\endgroup$ – user24855 Jun 9 '16 at 16:06
  • $\begingroup$ @Pig Huh, ok then. $\endgroup$ – nicael Jun 9 '16 at 16:07
  • $\begingroup$ Make sure you've seen those updated hints. $\endgroup$ – user24855 Jun 9 '16 at 16:08

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