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    LTheobald's Avatar
    LTheobald Posts: 1,051, Reputation: 127
    Ultra Member
     
    #1

    Apr 15, 2005, 06:57 AM
    Number Sequence Help
    Somebody at work has stumped the office with this:

    What is the next number?
    33 36 39 42 52 60 110


    Anyone got any ideas? I can't concentrate on my work because I keep thinking of this :) I'm even using Excel to type in mathmatical equations to find the answer :P
    CroCivic91's Avatar
    CroCivic91 Posts: 729, Reputation: 23
    Senior Member
     
    #2

    Apr 15, 2005, 08:16 AM
    Questions like these make no sense. For every number you can think of, I can make a logic equation that will say it's a "logical" next number.

    To make an example easy, let's look at sequence 1, 2, 3.
    You can say the next number is 4, because you're counting 1,2,3,4... you can also say the next number is 5 and after that 8, because 1+2=3, 2+3=5, 3+5=8.

    But you can also say the next number is 40.
    Why? If you look at the function
    p(x) = -24 + 78 x - (187x^2)/2 + (107x^3)/2 - (29x^4)/2 + (3x^5)/2
    and calculate p(1) you will get 1.
    p(2)=2
    p(3)=3
    p(4)=40

    But you can also say 70!
    Why?
    Take a look at h(x) = -54 + 169x - (397x^2)/2 + 111x^3 - (59x^4)/2 + 3x^5
    h(1)=1
    h(2)=2
    h(3)=3
    h(4)=70

    Basically, for any given number, you can find a "logic" for just THAT number to be the next in line.

    Lets say you want to prove you can find a logic for PI to be the next number in sequence.

    Just take a look at function
    g(x) = 4 - PI - (19*x)/3 + (11*PI*x)/6 + 4x^2 - PI*x^2 - (2x^3)/3 + (PI*x^3)/6
    g(1)=1
    g(2)=2
    g(3)=3
    g(4)=PI
    CroCivic91's Avatar
    CroCivic91 Posts: 729, Reputation: 23
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    #3

    Apr 15, 2005, 08:20 AM
    Oh... to answer your question. I would say the next number is 460.

    Reason is this function:
    p(x) = 152 - (579 x)/2 + (11738 x^2)/45 - (905 x^3)/8 + (919 x^4)/36 - (23 x^5)/8 + (23 x^6)/180

    p(8) = 460
    maressa7's Avatar
    maressa7 Posts: 1, Reputation: 1
    New Member
     
    #4

    Jun 24, 2013, 06:22 AM
    What's the next number in sequence 3,5,6,10,12,20
    InfoJunkie4Life's Avatar
    InfoJunkie4Life Posts: 1,409, Reputation: 81
    Ultra Member
     
    #5

    Jun 25, 2013, 02:19 AM
    3 - 5 - 6 - 10 - 12 - 20 - 24 - 40 - 48 - 80 - 96 - 160 - 192 - 320 - 384.. .

    ;)
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
    Expert
     
    #6

    Jun 25, 2013, 06:06 AM
    I know this is a really old question, but I do have the answer to the OP's question:

    Quote Originally Posted by LTheobald
    What is the next number?
    33 36 39 42 52 60 110
    Assuming that the OP accidentally left out one number in the sequence, so it is actually 33 36 39 42 46 52 60 110, this sequence is the number 42 written first in base 14, then base 13, then base 12, etc. The next number after 110 (which is 42 in base 6) is 132.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
    Expert
     
    #7

    Jun 25, 2013, 06:11 AM
    Quote Originally Posted by InfoJunkie4Life View Post
    3 - 5 - 6 - 10 - 12 - 20 - 24 - 40 - 48 - 80 - 96 - 160 - 192 - 320 - 384 . . .

    ;)
    Very good. And then 640, 768, 1280...

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