The following are the first twenty terms of a sequence: 1, 2, 3, 4, 5, 3, 7, 4, 6, 5, 11, 4, 13, 7, 5, 6, 17, 6, 19, 5, 7, 11, 23, 4, 10, 13, 9, 7, 29, 5, 31, 8, 11, 17, 7, 6, 37, 19, 13, 5, . . . 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. 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. I'll post the solution on next week's sequence. Last week's sequence (1, 2, 3, 1, 5, 6, 7, 2, 1, 10, . . .) was what's called the square-free part of n. That is to say, a(n) is the smallest positive (i.e., nonzero) divisor of n such that na(n) is a square. E.g., 18=2∙32 so (2)(18)= 22∙32=(2∙3)2, yielding a(18)=2. KWTsui solved it. Update: I've added another 20 terms to the sequence. Furthermore, here's a very strong hint: The sequence describes a certain relationship between n and a(n)! (i.e., a(n) factorial).
Monday, April 6, 2009
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4 comments:
is it that it's just the biggest factor (value-wise) of each number times the power to which it's raised (for example, 10 => 2 x 5^1 => 5^1 > 2 so you get 5 x 1 = 5; 12 = 3 x 2^2 => 2^2 > 3, 2 x 2 = 4)?
Oh, and this is Jared Kaliciak taking a break from Thermo.
yo! It was you who liked the passed around rose analogy concerning premarital sex, right? What did you think of the take today’s article from Desiring God had on it?
(If it wasn’t you, I am sorry for the confusion that this will now have brought on).
Oh. And I now realize that it wasn't an article on the actual website, it was a video.
I find it very interesting that Matt Chandler starts out by saying he didn't find evangelism and church compatiable (I hope that is correct) yet is now a lead pastor.
Jared, that's so complicated! I don't know what you mean. If post the next few terms (e.g., the 21st to 25th, maybe), then I can tell you if you're right or wrong.
Meredith, the only time I've ever heard the rose story before was from Matt Chandler's message at the Pastors Conference. I know that he didn't like it because it doesn't communicate grace, which I can agree with, but I still thought that it was a good apologetic (a good defense) for why people should not have premarital sex.
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