# A meaningful sequence of numbers

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?

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

$$51$$
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 famous Collatz Conjecture, except it involves always multiplying by $$3$$, and dividing by $$2$$.