[seqfan] Re: from Steven Finch about A087687
Olivier Gerard
olivier.gerard at gmail.com
Mon Jan 26 14:51:30 CET 2009
From Steven Finch:
Dear Martin,
This is precisely what I was seeking -- thank you! --
will you please post your formula in the OEIS entry
for A087687? I wish to cite this later.
If anyone in the group knows how to rigorously prove
such formulas, I would enjoy learning this!
With much appreciation,
Steve
On Mon, Jan 26, 2009 at 14:15, Martin Fuller
<martin_n_fuller at btinternet.com> wrote:
> Conjecture without proof:
>
> a(2^k) = 2^(k+ceil(k/2))
> For odd primes p, a(p^(2k-1)) = p^(3k-2) (p^k+p^(k-1)-1) and a(p^(2k)) = p^(3k-1) (p^(k+1)+p^k-1)
>
> This is the same as A062775 for odd n.
>
> PARI program to calculate A087687 directly:
> A087687(n)=local(v=vector(n),w);for(i=1,n,v[i^2%n+1]++);w=vector(n,i,sum(j=1,n,v[j]*v[(i-j)%n+1]));sum(j=1,n,w[j]*v[(1-j)%n+1])
>
> Martin Fuller
>
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