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Thread: Sequence numbers

  1. #1
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    Post Sequence numbers

    Hello again (Iím stuck again),

    Given the following E sequence: 1,2,1,3,2,4,2,6,3,8,3,12.....

    Sequence numbers-f3930876-da51-470c-8eb5-491463577a79.jpeg

    Iíve been trying this for a bit and canít seem to come up with a recurrence relation that makes sense so I can find the following numbers in the sequence.

    the numbers increases then decreases. Thats what is making me stuck.

    Help is much appreciated!
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  2. #2
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    Re: Sequence numbers

    Look at the critters this way:
    1,2
    1,3

    2,4
    2,6

    3,8
    3,12
    Then pretty obvious that next is:
    4,16
    4,24
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  3. #3
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    Re: Sequence numbers

    Quote Originally Posted by DenisB View Post
    Look at the critters this way:
    1,2
    1,3

    2,4
    2,6

    3,8
    3,12
    Then pretty obvious that next is:
    4,16
    4,24
    Wow. That makes so much sense. Thank you! After looking at that I was trying to come up with a recurrence relation for generating the sequence and nothing I came up with made sense. So Iím puzzled.

    for every second number I understand itís multiplied by two, and the first one is and addition of one after two numbers.
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  4. #4
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    Re: Sequence numbers

    @DenisB

    Can you elaborate on your sequence. I'm confused.

    A sequence is a function. I always thought for each integer in the domain P^+ there can only be assigned one unique value of the sequence hence 1-1 and onto. Your sequence is many-one.

    Edit: Actually the sequence <(-1)^n> has proved me wrong about 1-1. But it's not many-one.
    Last edited by PilgrimsPath; Dec 7th 2017 at 12:00 PM.
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  5. #5
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    Re: Sequence numbers

    It's two sequences running together.

    n,<2>,n,<3> for n=1

    n,<2n>,n,<3n> for n>1
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  6. #6
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    Re: Sequence numbers

    Quote Originally Posted by PilgrimsPath View Post
    @DenisB
    Can you elaborate on your sequence. I'm confused.
    It's not MY sequence!
    I simply showed a way to "look" at the mess!!
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  7. #7
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    Re: Sequence numbers

    So what is your "look" on the problem to formalise this mess?
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  8. #8
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    Re: Sequence numbers

    WhassaMatta you, Pilgrim?!

    1,2
    1,3

    2,4
    2,6

    3,8
    3,12

    4,16*
    4,24**

    2*2 = 4; 4*2 = 8; 8*2 = 16*
    3*2 = 6; 6*2 = 12; 12*2 = 24**
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  9. #9
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    Re: Sequence numbers

    Thanks from DenisB
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  10. #10
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    Re: Sequence numbers

    Let's call the sequence $a_n$ where $a_0$ is the first number.
    a_{n+4} = \left(\dfrac{3+(-1)^{n+1}}{2}\right)a_n+\dfrac{1+(-1)^n}{2}, a_0=a_2=1, a_1=2, a_3=3
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