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April 16th, 2011, 11:01 AM   #1
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Number of terms in a sequence of primes

Dear all,

I'm trying to figure out how many terms are in this sequence: , where is an odd prime. I can't see the answer immediately, so I tried some smaller sequences:

i) For (ie) : There are terms.

ii) For (ie) : There are terms.

So for terms, I reasoned that there'd be terms. But the correct answer is .

Where have I gotten wrong? This may seem an easy question, but it's from a more complicated question so I thought to post it here.

Thank you very much1
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April 16th, 2011, 11:42 AM   #2
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Re: Number of terms in a sequence of primes

this is actually an arithmetic progression question, p being an odd prime doesn't interfere in the answer.

dividing the sequence by 2 yields , which has obviously terms, the same number of terms of the original sequence.

Where did "k" come from anyways?
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April 17th, 2011, 08:31 AM   #3
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Re: Number of terms in a sequence of primes

Thanks for your response, proglote.

So why does the solution say that there are terms? And I used to illustrate my reasoning when we had terms (so that I didn't have to write ).

In any case, I asked the original question since I am trying to figure out these two steps for a question on number theory:



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April 17th, 2011, 10:41 AM   #4
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Re: Number of terms in a sequence of primes

The solution could possibly be taking into account zero as the first term. Otherwise you've got it all right I believe
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April 17th, 2011, 11:17 AM   #5
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Re: Number of terms in a sequence of primes

The statement is also:



k!! is a double factorial
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April 19th, 2011, 01:00 PM   #6
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Re: Number of terms in a sequence of primes

Quote:
Originally Posted by mrtamborineman10
The solution could possibly be taking into account zero as the first term. Otherwise you've got it all right I believe
Thanks for the replies.

@mrtamborineman10: Could you please explain what you mean by zero as the first term?

We have:
, where the RHS starts with . Where would the 0 appear?

@Hoempa: We haven't done double factorials so that confuses me a bit. Could you explain without double factorials?
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