Starting t Today (Update: awkward wording fixed) will start tradition of uncertain length, where I'll post sequences. I'll post the answers on the following week's sequence. Anyway, the follow following (Update: conjugated the verb) are the first forty terms of a sequence: 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, . . . It may be of interest, though probably unhelpful in determining the pattern, that the limit at infinity of the sequence does not exist, though maxnє{1,2,3,4, . . .}{a(n)}=∞. Therefore, it follows that the derivative of the mystical curve of best fit is also non-existent at infinity. Same idea as the other sequences. Describe the pattern of the sequence. If you use a search engine, please don't submit it in the comments. It's pretty tricky. I think you'll need a hint. So, if it hasn't been solved by Thursday, I'll give a hint then. Also, if you ask a polar question (i.e., a yes/no question), I will probably answer it if it relates to this sequence. Update: Hint: Think prime numbers.
Monday, March 9, 2009
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4 comments:
I've added the hint to the body of the entry.
The value of the i-th term of the sequence is the number of prime factors that i has.
Well done, KWTsui. Did you need the hint?
Not really, but it reminded me to take a second look when I couldn't solve it the first time (I counted the multiplicities at first, so I got confused when I got to a(4)=1...). Thanks for these entertaining puzzles!
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