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Topic: Asimov Sequence (Read 464 times) |
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Speaker
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Asimov Sequence
« on: Sep 19th, 2003, 6:26pm » |
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I got this out of a short story by I. Asimov. What is the next number in the sequence?
8, 5, 4, 9, 1, 7, *,
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otter
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Re: Asimov Sequence
« Reply #1 on: Sep 19th, 2003, 8:47pm » |
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:: 6. Then 3, 2, 0. When spelled out in English, the numbers are in alphabetical order. ::
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| « Last Edit: Sep 19th, 2003, 8:48pm by otter » |
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Speaker
Uberpuzzler
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Re: Asimov Sequence
« Reply #2 on: Sep 19th, 2003, 8:52pm » |
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Well done.
How about another?
1, 2, 6, 12, 60, 420, 840, *
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| « Last Edit: Sep 19th, 2003, 8:57pm by Speaker » |
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They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
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otter
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Re: Asimov Sequence
« Reply #3 on: Sep 19th, 2003, 9:26pm » |
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on Sep 19th, 2003, 8:52pm, Speaker wrote:Well done.
How about another?
1, 2, 6, 12, 60, 420, 840, * |
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::2,520. I'll admit I didn't know the answer, but a buddy of mine knew right away. Something about "roots of prime powers", which I'll confess I still don't fully understand.::
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
and know the place for the first time.
T.S. Eliot
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Speaker
Uberpuzzler
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Re: Asimov Sequence
« Reply #4 on: Sep 19th, 2003, 9:31pm » |
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Your answer is correct, but the reason is different. At least, as far as I know it has nothing to do with what your friend is describing. But, stranger things have happened than me not understanding the math in a problem.
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Sir Col
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Re: Asimov Sequence
« Reply #5 on: Sep 20th, 2003, 3:40am » |
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I didn't get it from the sequence myself, until I peeked at otter's answer; and I recognised that number...
::2520 is the smallest number that is evenly divisible by 1,2,3,...,10; well it works for 1,2,...,9 actually. So I would have to disagree with the sequence, I would suggest that it goes: 1,2,6,12,60,60,420,840,2520,2520,27720,...
In other words, the nth term in the sequence is the smallest number that is evenly divisible by 1,2,...,n. ::
I wonder if there's a formula for that last sequence? 
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Speaker
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Re: Asimov Sequence
« Reply #6 on: Sep 21st, 2003, 4:59pm » |
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Yes. Sir Col you are right on all counts. I have no equation, and debated on whether to include the repeats, but Issac left them out so I did too. 
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otter
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Re: Asimov Sequence
« Reply #7 on: Sep 21st, 2003, 5:43pm » |
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on Sep 20th, 2003, 3:40am, Sir Col wrote:I didn't get it from the sequence myself, until I peeked at otter's answer; and I recognised that number...
::2520 is the smallest number that is evenly divisible by 1,2,3,...,10; well it works for 1,2,...,9 actually. So I would have to disagree with the sequence, I would suggest that it goes: 1,2,6,12,60,60,420,840,2520,2520,27720,...
In other words, the nth term in the sequence is the smallest number that is evenly divisible by 1,2,...,n. ::
I wonder if there's a formula for that last sequence? |
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Here's an explanation (at least I'm told it's an explanation). The thread (going back to the first post) apparently explains the nature of the sequence. I make no claims to understand it.
http://mathforum.org/discuss/sci.math/a/m/488534/489693
Icarus, can you shed some light on this one?
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| « Last Edit: Sep 21st, 2003, 5:48pm by otter » |
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
and know the place for the first time.
T.S. Eliot
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