[seqfan] Re: A088144 and A076409 (esp the latter)

[Maximilian Hasler]

On Thu, Feb 24, 2011 at 3:24 PM, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:

> proof that, for  4k+3  primes, there are more quadratic
> residues in the interval  [1,2k+1]  than there are in
> [2k+2,4k+2].  These numbers also merit a place in OEIS:
>
> Number of q.r.s in the first half:
> 1, 2, 4, 6, 7, 9,12,14,19,18,21,22,25,28,31,
>
> Number of q.r.s in the last half:
> 0, 1, 1, 3, 4, 6, 9, 9,10,15,14,17,16,23,22,
>
> Excess of first half over last half:
> 1, 1, 3, 3, 3, 3, 3, 5, 9, 3, 7, 5, 9, 5, 9,

I added the first 2 among these 3 as A186708 and A186709;
the last one (=their difference)  is already there, as http://oeis.org/A178154.
Their sum is A104635 = [p/2] = (A002145 - 1)/2
which yields several (straightforward) relations between all of these.

Maximilian