[seqfan] Re: Close sequences again

Michael Porter ic_designer at verizon.net
Tue Oct 20 10:11:55 CEST 2009

> (Sum of the quadratic non-residues of prime(n) - Sum of the quadratic

> residues of prime(n)) / prime(n).  I discovered that this was equivalent to

> (sum ( floor  (j^2 / prime(n))), j = 1:prime(n) - 1) - floor ((prime(n) -

> 2)(prime(n) - 1) / 3) and that this could be extended to the naturals.  

That seems like a non-trivial result, so I'm glad to see you have already added it to OEIS (A165951).  But for a(1) and a(2), prime(n)=2 and 3, the expression evaluates to -1/2 and 1/3, right?

> A166128
> A166129
> A166130
> A166468

A166468 is the one we were discussing earlier, and if I read it correctly, A166128 is just prime(n)-1 with a(1) set to 0, so a similar argument applies.  I can't seem to get to A166129 and A166130.
- Michael

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