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The following sequence of numbers is related to a famous Conjecture.

17, 188, 94, 47, 518, 259, 37, 408, 204, 102, ?

Could you find the next number in the sequence?

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  • $\begingroup$ Are you sure the 37 isn't a typo? $\endgroup$ Oct 3 '20 at 19:37
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    $\begingroup$ I am sure - I copied and also calculated it:) $\endgroup$
    – Moti
    Oct 3 '20 at 19:38
  • $\begingroup$ sequence is known in OEIS: oeis.org/A057614 $\endgroup$
    – ThomasL
    Oct 3 '20 at 19:55
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The next number is:

$51$

The pattern:

If the last term in the sequence so far is prime, multiply it by $11$ and add $1$, and if the last term in the sequence so far is composite, divide it by its smallest prime factor. (equal to $2$ except in one case, $259 \rightarrow 37$) The resulting number is the next term in the sequence.

The related conjecture is...

...the famous Collatz Conjecture, except it involves always multiplying by $3$, and dividing by $2$.

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