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A friend of mine gave me this riddle.

Find the next number of the sequence:

293, 313, 331, ...

Let's see who can do better than I did.

Hint:

There is a new number:

263, 293, 313, 331, ...

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  • $\begingroup$ Did your friend give any additional numbers or clues? With three numbers there will be many sequences that may fit, but not be the intended answer. for example: rot13(svefg nqq gjragl, gura nqq rvtugrra, nqq fvkgrra naq fb ba) $\endgroup$
    – P1storius
    May 25 '20 at 6:57
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    $\begingroup$ Yes, but he gave me the previous number' not the next one. I will edit the question and add the new number. $\endgroup$
    – omri klein
    May 25 '20 at 7:01
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    $\begingroup$ does this is related to 10-happy-prime ? $\endgroup$
    – Swati
    May 25 '20 at 14:28
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The sequence is:

A list of happy prime numbers

So a longer list includes:

7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487.

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  • $\begingroup$ Great! thank you. $\endgroup$
    – omri klein
    May 25 '20 at 18:14
  • $\begingroup$ @omri klein Make sure you not to tell your friend that you had help from a community with solving it $\endgroup$ May 25 '20 at 18:15
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The sequence of prime numbers follows the pattern below

›! The next number is 337.

263 4x+3

293 4x+1

313 4x+1

331 4x+3

337 4x+1

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  • $\begingroup$ Nice idea, but check out the last answer, it's the right answer. $\endgroup$
    – omri klein
    May 25 '20 at 19:11
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    $\begingroup$ From the number you gave I drew the conclusion one prime 4x+3 two primes 4x+1 one prime 4x+3 and two primes 4x+1. $\endgroup$ May 25 '20 at 20:39

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