[seqfan] Re: Generally known (to those who know of such things)
Victor S. Miller
victorsmiller at gmail.com
Fri Nov 20 19:52:44 CET 2009
I don't quite understand the notation in your sum:
Do you mean that u(t) = sum(k=1 to t) k*p1[k]
Where p1[k] is the k-th prime =1 mod 4?
In any case this may be related to "Chebyshev's bias" there are more
primes that are 3 mod 4 than 1 mod 4.
Victor
Sent from my iPhone
On Nov 20, 2009, at 11:39 AM, "Meeussen Wouter \(bkarnd\)" <wouter.meeussen at vandemoortele.com
> wrote:
> I don't understand, again, why the primes (p1) of form 4n+1 differ in
> behaviour from those (p3) of form 4n+3 in the following:
>
> u=Sum=1..p1; k (p1-k) ) is strictly increasing in function of p1,
> while
> v=Sum(k=1..p3; k (p3-k) ) is not (in function of p3).
>
> v is descending from v(37) to v(38)
> {4, 28, 66, 190, 322, 558, 946, 1316, 1888, 2278, 2982, 3476, 3652,
> 5768, 5992, 8636, 9170, 10008, 12382, 13366, 15698,
> 16826, 20628, 21492, 22788, 26314, 26786, 32026, 33132, 37872, 39566,
> 40752, 47892, 54114, 55608, 61766, 71082, 70464
>
> I checked 'u' way up to 10,000 and found no 'drops'.
>
>
> Wouter.
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