Results 1 to 3 of 3

Math Help - Looking for help on a sequence question - interesting problem

  1. #1
    Newbie
    Joined
    Aug 2014
    From
    Australia
    Posts
    2

    Lightbulb Looking for help on a sequence question - interesting problem

    Hi Everyone,

    I hope this is the right place for a sequence question but I'm stuck. I can solve it programatically but not mathematically and think I'm missing something.

    A series is formed with an original value of 2 and each following term in the sequence given by the previous term + the highest prime factor of the previous term so...
    an+1= an + pn. The first term a1 is 2.

    The series is pretty easy to construct and the following terms are the first bunch 2,4,6,9,12,15,20,25,30,35,42,49,56,63,70,77,88,99, 110,121,132,143...

    The question is: What is the largest value of n such that an is a four digit number. As I said I can loop through and brute force the thing using a computer but there's got to be a pattern I'm missing.

    Over to all you clever math people.

    Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,091
    Thanks
    315

    Re: Looking for help on a sequence question - interesting problem

    It's not hard to show that the value of the largest 4-digit number in this series is 99 x 101 = 9999. But as for the value of n, hmmm... I need to think about it.

    EDIT - OK, I thought about it, and I believe the value of n is 99+101-2 = 198.

    The first step is to find the value the prime to use - it's either the largest prime whose square <= 10000, or the next higher prime after that. In this case the square root of 10000 = 100, so it's either 97 or 101. Since 97x101 = 9797, and we can continue to add 101's to it and still stay under 10000, the prime to use is 101. Next: 10000/101 = 99.0099, so the second factor is 99.
    Last edited by ebaines; August 8th 2014 at 05:54 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2014
    From
    Australia
    Posts
    2

    Re: Looking for help on a sequence question - interesting problem

    I knew I was thinking about it badly I just couldn't see how to approach it.

    Thanks heaps
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. interesting probability puzzle involving out-of-sequence series
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 20th 2010, 10:58 AM
  2. Limit of an interesting sequence
    Posted in the Math Challenge Problems Forum
    Replies: 8
    Last Post: November 4th 2010, 06:38 PM
  3. sequence problem (more of a limits question)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 28th 2010, 01:05 AM
  4. Find an "interesting" Cauchy sequence.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 6th 2009, 05:54 AM
  5. Interesting sequence - find closed form
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 30th 2009, 08:38 AM

Search Tags


/mathhelpforum @mathhelpforum