A simple one this week.  Mathematicians often refer to the following list of numbers as an ‘Eban’ sequence – without looking up that term, can you figure out the next number in the sequence?

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, ??

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took.  Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.


  1. Hmm, after a couple of minutes I decided I have one digit of the solution and not enough entropy to decide the other among a couple plausible solutions.

    BTW, going by the letter of the instructions, one might be permitted to look up the sequence itself …

  2. In Volapük the sequence would start 1, 3, 4, 5, 6, 8, 9, 100, 101, 103 etc.

    In Esperanto it starts 1, 2, 3, 4, 5, 8, 9, 1000, 1001, 1002, 1003, 1004, 1005, 1008, 1009, 2000, 2001 etc.

    In Arabic it includes all integers.

    1. To be pedantic, I reckon my answer is about 3.8 lower than everyone else…
      I have to say, I looked up the term and while it’s clever, I was disappointed. Being a maths degree holder and never hearing of this before I expected something a little more mathematical.

  3. A better puzzle might have been to take this to the 14th term, and ask for the next… The second and rather intriguing jump in the numbers…

    1. Same here. Had it almost before I read the question then looked it up and was right but my reasoning would have fell apart after another couple of iterations.

  4. OK, I had to look it up, then realised the significance of the term…

    Meanwhile, since we’re covering different languages, to the best of my understanding, to a Welsh speaker the first few would be:

    1, 2, 3, 5, 7, 8, 9, 20, 21, 22, 23, 25, 27, 28, 29

    Depending on who you ask, the next number in the sequence could be either 60 or 100…

  5. French:
    1, 3, 5, 6, 8, 10, 18, 20, 23, 25, 26, 28, 1000000, …

    1, 2, 4, 5, 8, 1000, 1001, 1002, 1004, 1005, 1008, …

    I think, I could have made a mistake in there…

  6. I got it straight away, like not even a second. Then I looked it up (because I had never heard of such a thing) and found out that
    A- I was right in the next number AND
    B- I had no reason to be correct other than dumb luck, because I had no idea why that would be the next number other than my mathematically challenged brain thought it sounded good.

    Still, I claim victory!

  7. I found a rather short mathematical expression that fits this sequence exactly and through it I’ve found a candidate for the 12th number. Obviously it’s not the solution, but hey…

  8. i know what the next one is and i did check it out and i did get the right answer but i also thought it was a math pattern.but i was mistaken :/ it was still fun and it took a few seconds

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