Arithmetic quiz

Discussion in 'Physics & Math' started by arfa brane, Feb 19, 2017.

  1. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    What's the next number in the sequence:

    1, 2, 4, 5, 8, 9, 10, 13

    ?
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. DaveC426913 Valued Senior Member

    Messages:
    7,244
    Spoiler:[ 16 ]
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. river

    Messages:
    9,793
    17
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    A clue: some numbers are "missing". There is a reason they are.
     
  8. river

    Messages:
    9,793
    yes

    to distract
     
  9. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    Chuckle.
     
  10. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    The reason is to do with numbers being sums of powers of numbers.
    Including zero as a number.
     
  11. river

    Messages:
    9,793
    hmmm... yet 0 was not included in the , sequence .

    I still stand by my answer as 17 .

    you haven't told me I'm wrong arfa .
     
  12. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    Ok, you're wrong.

    And BTW, 17 must be an even number + 1. All powers of 1 are equal to 1. I've now told you plenty enough.

    Ed. I concur 0 should be in the sequence, I guess it isn't because "trivially" 0 is the sum of an infinite series of any power of 0. So the first number in the sequence, 1, isn't because one of the powers is of itself, but the rest can all be 0.
    However, only one power of 0 is needed in any sum. I can't believe I just typed all that

    But, there's the axiom that things with an = sign between them need not be in the same space.
    'sigh' I guess you have to say that yes, the sequence should start with 0 because it's the first number that can be written as a sum of powers of numbers, but they all have to be 0 . . .
     
    Last edited: Feb 19, 2017
  13. river

    Messages:
    9,793
    now I can move on .
     
  14. river

    Messages:
    9,793
  15. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    I'm going to step away from the computer now, while keeping my hands where I can see them.
     
  16. river

    Messages:
    9,793
    so I'm wrong again . dam
     
  17. river

    Messages:
    9,793
  18. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    Try this: write down the smallest sum of squares of numbers each equal to the first n natural numbers (include 0 as a sum of two squares if you must).
    A sum has at least two numbers in it to be a sum. But these sums include the square of 0.

    And that's the answer, the numbers in the sequence are all the smallest sums of squares, i.e. sums of two squares, which is why some numbers are missing.
     
  19. DaveC426913 Valued Senior Member

    Messages:
    7,244
    Was my answer in post 2 correct or no?
     
  20. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    7,477
    Yes, it was correct.
     
  21. arfa brane call me arf Valued Senior Member

    Messages:
    5,365
    I didn't see any answer in post #2.
     
  22. DaveC426913 Valued Senior Member

    Messages:
    7,244
    That's how you hide spoilers. Highlight the text inside the brackets.
     
  23. James R Just this guy, you know? Staff Member

    Messages:
    30,644
    Or do this:
    This is a spoiler. Enclose text in [spoiler][/spoiler] tags to get this effect.
     

Share This Page