Discussion in 'Physics & Math' started by arfa brane, Feb 19, 2017.
What's the next number in the sequence:
1, 2, 4, 5, 8, 9, 10, 13
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Spoiler:[ 16 ]
A clue: some numbers are "missing". There is a reason they are.
The reason is to do with numbers being sums of powers of numbers.
Including zero as a number.
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 .
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 . . .
now I can move on .
I'm going to step away from the computer now, while keeping my hands where I can see them.
so I'm wrong again . dam
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.
Was my answer in post 2 correct or no?
Yes, it was correct.
I didn't see any answer in post #2.
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