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Next Numbers Please #9 (Posted on 2017-08-23) Difficulty: 3 of 5
What are the next four numbers in the sequence 1, 2, 3, 4, 5, 3, 7, 4, 6, 5, 11, 4, __, __, __, __?

When does the number 12 first appear in the sequence?

See The Solution Submitted by Brian Smith    
Rating: 3.6667 (3 votes)

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Solution re: When 12 appears | Comment 4 of 9 |
(In reply to When 12 appears by Math Man)

No, 512 (ie, 2^8) is not the answer to part 2.  The 512th term is 8, because 512 divides 8! but not 7!.


However, I see the error of my ways.  The prime factors of 12 are 2 and 3, so the first occurrence of 12 is either a power of 2 or a power of 3.  2^10 (ie, 2048) and 3^5 (i.e. 243) both divide 12! but not 11! 

243 is smaller, so the 243rd term is the first occurrence of 12 in the series.  Final answer.

  Posted by Steve Herman on 2017-08-23 20:23:14
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