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What is the next number in the following sequence: 0, 4, 8, 21, 52, 65, 96, ?

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!

This puzzle was shared with me several years ago by my Computer Science department head, Ralph Stanton.

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  • $\begingroup$ This is a low-effort puzzle with a trivially Googleable solution, so is likely to attract downvotes. See this meta post $\endgroup$
    – fljx
    Commented Oct 18, 2023 at 7:52
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    $\begingroup$ If you go to the tag wiki, you'll find a link to this meta question, where the top answer gives exactly one general guideline for number sequence puzzles. It's a very good idea to follow that guideline. A003608. $\endgroup$
    – Bass
    Commented Oct 18, 2023 at 7:53
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    $\begingroup$ @Bass I do puzzles because they are challenging and fun. I hope that when people read my puzzles they will try to solve them on their own without trying to find the solution online. What’s the fun in simply searching online for a solution? If at least one person reads my puzzle and has an enjoyable time solving it by themselves, I will be happy. $\endgroup$
    – Will.Octagon.Gibson
    Commented Oct 18, 2023 at 8:28
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    $\begingroup$ @fljx When I was shown this puzzle many years ago, I had a sense of satisfaction when I eventually solved it. I post this puzzle with the hope that at least some people will also derive satisfaction from it. $\endgroup$
    – Will.Octagon.Gibson
    Commented Oct 18, 2023 at 8:33
  • $\begingroup$ This question can be asked in a different way too. We can interpret $4$ as $04$. Then the series would be $0$, $40$, $44$, $84$, $88$, $29$, $33$, $?$ $\endgroup$
    – Etack Sxchange
    Commented Oct 23, 2023 at 19:32

1 Answer 1

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The next number in the sequence is

1.

Because,

one simply adds 4 to the number, and then reverses the order of the sum. 96 + 4 = 100, 100 reversed becomes 001 or simply 1. Continuing on would provide the numbers 5, 9, 31, 53, 75, 97, 101, 501, etc.

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