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?

(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.