# Here's a puzzle that's easy only after you hear the solution: What comes after 3, 4, 6, 8, 12, 14?

Originally published at: Here's a puzzle that's easy only after you hear the solution: What comes after 3, 4, 6, 8, 12, 14? | Boing Boing

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# 3 , 4 , 6 , 8 , 12 , 14 , 18, 20, 24, 30, 32, 38, 44, 62.

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What comes after 3, 4, 6, 8, 12, 14?

Another number.

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Any number. This is easy!

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p(n)+1, where p(n) is the nth prime number.

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Job interview, Go to the bathroom, Look up oeis, … what’s the next in this sequence?

22273 is the largest prime in the Bible: Numbers (appropriately enough) 3:43

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I have a logical brain,but not a sufficiently mathematical one,so I do not enjoy number sequence puzzles. My family do regular quizzes and my suggestions for questions are regularly quashed as too difficult.
Here’s a number sequence for you.
99, 14, 8, 21, … what?

The answer is 55. They are the house numbers of the buildings I have lived in, in order. This sequence makes as much sense to me (as a question for other people) as some of the sequences posed.

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Or 3, 4, 6, 8, 12, 14 , 15, 18, 21, 22, 24, 28, 30, 30, 33, 38, 39, 38, 42, 48, 48, 46, 51, 58, 57, 54, 60, 68, 66, 62, 69, 78, 75, 70, 78, 88, 84, 78, 87, 98, 93, 86, 96, 108, 102, 94, 105, 118, 111, 102, 114, 128, 120, 110, 123, 138, 129

Or 3, 4, 6, 8, 12, 14 , 15, 16, 18, 20, 24, 26, 27, 30, 32, 35, 36, 38, 39, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 78, 80, 81, 84, 86, 87, 88, 90, 92, 95, 96, 98, 100, 102, 104, 108, 110, 112, 114, 116, 117, 119, 120, 122, 123, 124, 125, 126, 128, 130, 132, 135, 138, 140, 143, 144

Or 3, 4, 6, 8, 12, 14 , 18, 20, 24, 30, 32, 38, 42, 48, 54, 60, 62, 68, 72, 80, 84, 90, 98, 108, 110, 132, 138, 140, 150, 180, 182, 198, 252, 318, 360, 398, 468, 570, 572, 930, 1722

Or 3, 4, 6, 8, 12, 14 , 15, 16, 18, 20, 21, 24, 28, 30, 32, 36, 40, 42, 45, 48, 54, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 100, 105, 108, 112, 120, 124, 126, 128, 132, 135, 136, 140, 144, 147, 150, 154, 156, 160, 162, 165, 168, 176, 180, 182, 186, 189, 192

Or 3, 4, 6, 8, 12, 14 , 20, 24, 38, 54, 62, 80, 90, 110, 138, 150, 164, 168, 192, 194, 272, 278, 314, 332, 348, 398, 402, 434, 500, 572, 642, 644, 720, 728, 762, 798, 812, 860, 864, 878, 920, 992, 1020, 1022, 1070, 1092, 1098, 1118, 1130, 1182, 1202, 1230, 1260, 1308

You get the point

http://oeis.org/search?q=3%2C+4%2C+6%2C+8%2C+12%2C+14&language=english&go=Search

I was good at those ‘what comes next’ questions but always sort of hated them. There’s no definite structure to a small list of numbers, sure you could come up with a least complex explanation, but you need more information to know if it is meaningful. For example,
2, 4, 8, 16, 32, and now… 63
http://oeis.org/A006261
Because we were counting the number of regions you get when you cut a circle with n straight lines, not powers of 2.

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Here’s one that stumped me:
14, 18, 23, 28, 34, 42, 50, 59, 66, 72, 79, 86, 96, 103, 110, 116, …
I couldn’t get it despite being at 116 at the time.

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Matt Gaetz

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Yeah, his number is up…

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3, 4, 6, 8, 12, 14… What comes next?

15, 16… But really, I’d be more worried about the numbers you’re missing earlier.

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So you’re saying his days as a politician are numbered?

Because so many of us have now got his number, so he can’t come out as Number 1 in an election anymore?

(Ugh, I’m numb now, or number than I was before.)

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HAL could get that one easily.

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or maybe an emoji

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The answer always is (or can be) 42. Just fit a polynomial curve to the data.

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4, 8, 15, 16, 23, 42

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Normally I don’t even try to do puzzles like this because I’m no good at them, but one of my OCD/coping mechanisms focuses on prime numbers - I recite them silently to myself in stressful situations (and no, that’s not crazy, it’s very relaxing! ) so this one was pretty easy for me.

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Came here to say the same.

And, as Steve notes, include the number you want next. It’s almost trivial in Excel for series up to 6 (total those given and asked for), so doesn’t work quite as well for this example.

But if you don’t want to pick the next term yourself, Excel can do that too:

Turns out term number 7 is -5. Took me less than a minute.
Or “different” equation, same result of -5

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