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) $\endgroup$– P1storiusCommented May 25, 2020 at 6:57
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1$\begingroup$ Yes, but he gave me the previous number' not the next one. I will edit the question and add the new number. $\endgroup$– omri kleinCommented May 25, 2020 at 7:01
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1$\begingroup$ does this is related to 10-happy-prime ? $\endgroup$– SwatiCommented May 25, 2020 at 14:28
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2 Answers
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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.
answered May 25, 2020 at 18:13
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$\begingroup$ @omri klein Make sure you not to tell your friend that you had help from a community with solving it $\endgroup$ Commented May 25, 2020 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
answered May 25, 2020 at 18:36
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$\begingroup$ Nice idea, but check out the last answer, it's the right answer. $\endgroup$ Commented May 25, 2020 at 19:11
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1$\begingroup$ 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. $\endgroup$ Commented May 25, 2020 at 20:39