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Find a pattern for the following sequence. 1,1,3,1,3,5,7,1,3,5,7.....

Let n= the nth number.

Find the nth number of this series

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Sorry, the ellipsis are bugging me a little, is it 1,3,1,3,5,1,3,5,7,1,3,5,7,9,... or 1,3,1,3,5,1,3,5,7,1,3,5,7,11,...? I mean, is just odd numbers or prime numbers? –  Ana Galois Sep 18 '13 at 23:16
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@AnaGalois: $1$ is not prime. I have my guess what it should be. –  Ross Millikan Sep 18 '13 at 23:24
    
@RossMillikan silly me, you are right, wasn't considering that –  Ana Galois Sep 18 '13 at 23:27
    
You still have the $7$ in the seventh place. Do you mean that? It breaks up the pattern I see. –  Ross Millikan Sep 18 '13 at 23:30
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1 Answer

up vote 3 down vote accepted

Hint: It appears the first $7$ should not be there. Without it, you have one odd number, then two, then three, then four, etc. The block you are in can be recovered from the triangular numbers. If you really mean it with both $7$'s I don't see the pattern.

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The lengths of the sequences of odd numbers might be the powers of two... –  Abel Sep 18 '13 at 23:29
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