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Thread: 1,3,7,25,103,?

  1. #1
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    1,3,7,25,103,?

    What is the next no. , cant solve this one
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    Re: 1,3,7,25,103,?

    Quote Originally Posted by burrraaahhh View Post
    What is the next no. , cant solve this one
    Here is the only answer I know.
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    Re: 1,3,7,25,103,?

    321 is the next number
    Here's what I did.
    Plotted the points (1, 1), (2, 3), (3, 7), (4, 25) and (5, 103).
    Turns out that a quartic function fits this data perfectly (R^2=1)
    Then two options from there.
    Method 1: Look at a table of differences so that the 4th row is constant (34) and complete the table backwards to get 321
    Method 2: Sub x=6 into the quartic function found (by regression on a GC) and get 321.
    The quartic equation is (17/12)* x^4 - (73/6)* x^3 + (463/12)* x^2 - (299/6) * x + 23
    Last edited by Debsta; Mar 13th 2016 at 04:18 PM.
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    Re: 1,3,7,25,103,?

    Quote Originally Posted by Debsta View Post
    321 is the next number
    Here's what I did.
    Plotted the points (1, 1), (2, 3), (3, 7), (4, 25) and (5, 103).
    Turns out that a quartic function fits this data perfectly (R^2=1)
    Then two options from there.
    Method 1: Look at a table of differences so that the 4th row is constant (34) and complete the table backwards to get 321
    Method 2: Sub x=6 into the quartic function found (by regression on a GC) and get 321.
    The quartic equation is (17/12)* x^4 - (73/6)* x^3 + (463/12)* x^2 - (299/6) * x + 23
    The problem with this is that we can use any polynomial fit larger than degree 4 and still get an answer...321 is the only possible fit for a quartic, but you can do a quintic, etc. fit as well. Unless there is some kind of pattern that can be spotted the problem is basically impossible. Plato gave a link that has a huge list of known series but it obviously doesn't cover all of them.

    -Dan

    Addendum: As another example I can easily come up with a next number: We have 1, 3, 7, 25, 103. 103 is the first term, followed by a 0, followed by the second term. So the next term could easily be the second term followed by a 0 followed by third term: 307.
    Last edited by topsquark; Mar 13th 2016 at 05:26 PM.
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    Re: 1,3,7,25,103,?

    Yeah sure. There's a infinite number of answers that can be justified somehow.
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    Re: 1,3,7,25,103,?

    Quote Originally Posted by Debsta View Post
    Yeah sure. There's a infinite number of answers that can be justified somehow.
    But still your answer is not in the form of a sequence. The question is written in a form that is a usual sequence. It says nothing about a fit,
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    Re: 1,3,7,25,103,?

    Isn't a sequence just an ordered list of numbers that follow some rule?
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    Re: 1,3,7,25,103,?

    It doesn't even have to follow any rule.
    Last edited by Archie; Mar 13th 2016 at 09:35 PM.
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    Re: 1,3,7,25,103,?

    I wonder what the "correct" answer was , burrraaahhh?
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    Re: 1,3,7,25,103,?

    Quote Originally Posted by Debsta View Post
    I wonder what the "correct" answer was , burrraaahhh?
    Once again, there is no correct answer. If 1,3,7,25,103,X, where X can be any number whatsoever, is a correct answer. That is why you will never see such a question, without qualifiers such as "a recursive", on a professionally constructive test.
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    Re: 1,3,7,25,103,?

    Hence the use of " ". I was just wondering what answer was given/expected by the writer of the question.
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    Re: 1,3,7,25,103,?

    Stephen, you play the Number Sequence game? Is this generated from the game? If yes, which level? I could help check on the logic.
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    Re: 1,3,7,25,103,?

    Who d'hell is Stephen? This thread getting sillier by the minute...
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    Re: 1,3,7,25,103,?

    1 * 1 +2 -> 3
    3 * 2 +1 -> 7
    7 * 3 +4 -> 25
    25*4 +3 -> 103
    So we have (1, 2) -> (2, 1) then (3, 4) -> (4, 3) which leads to the next one (5, 6) and even (6, 5)
    103*5+6 -> 521
    521*6+5 ->...
    Is this correct friend ?
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  15. #15
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    Re: 1,3,7,25,103,?

    That certainly is a correct answer, and a clever one, but, as others have said, there is no one correct answer.
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