# Arithmetic quiz

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

1. ### arfa branecall me arfValued Senior Member

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What's the next number in the sequence:

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

?

3. ### DaveC426913Valued Senior Member

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Spoiler:[ 16 ]

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17

7. ### arfa branecall me arfValued Senior Member

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A clue: some numbers are "missing". There is a reason they are.

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yes

to distract

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Chuckle.

10. ### arfa branecall me arfValued Senior Member

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The reason is to do with numbers being sums of powers of numbers.
Including zero as a number.

11. ### river

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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 branecall me arfValued Senior Member

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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

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now I can move on .

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26

15. ### arfa branecall me arfValued Senior Member

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I'm going to step away from the computer now, while keeping my hands where I can see them.

16. ### river

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so I'm wrong again . dam

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12

18. ### arfa branecall me arfValued Senior Member

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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. ### DaveC426913Valued Senior Member

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Was my answer in post 2 correct or no?

20. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

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Yes, it was correct.

21. ### arfa branecall me arfValued Senior Member

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I didn't see any answer in post #2.

22. ### DaveC426913Valued Senior Member

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That's how you hide spoilers. Highlight the text inside the brackets.

23. ### James RJust this guy, you know?Staff Member

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