# Sequence abundent in primes

Max Alekseyev maxale at gmail.com
Thu Aug 2 14:41:51 CEST 2007

```Philippe,

I do not know if your particular sequence was studied but in general
the prime generating polynomials are known beasts. For instance, take
a look at:
http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
and
http://www.recmath.org/contest/PGP/index.php

Max

On 8/2/07, Lallouet <philip.lallouet at wanadoo.fr> wrote:
>
>
> The well known euler's sequence n^2-n+41 contains 999 terms < 10^6; 580 of
> them are primes giving a ratio of 58,06%
>
> Studying the matrix :
>
> r
> 1          1      3      6      10      15     .      .
> 2          2      5      9      14         .      .      .
> 3          4      8     13        .         .      .      .
> 4          7    12        .        .         .      .      .
> 5        11       .        .        .         .      .      .
>
> I found that the diagonal r-c=399 (r for row, c for colomn) was peculiarly
> rich in primes.
>
>   r
> 399    79801      80202      80604
> 400    80201      80603      81006
> 401    80602      81605      81409
>
> The formula 2*n^2-4*n-197 gives all the numbers of this diagonal for n>=201.
> For smaller values of n we get smaller results, the tens
>
> first beeing negative.
>
> The last value < 10^6 is obtained for n=708; absolute values of 448 of them
> are primes giving a ratio of 63,27%.
>
> That is better than the Euler's record, at least in this limit .Moreover the
> source of this sequence is simpler than Ulam's ones.
>
> So, I am very surprised not to have read anything about it nor in books,nor
> on the web.
>
> May somebody telle me if this sequence has been already studied and
> published?
>
> I join a complete list of the 708 first terms of the sequence.
>
> As this message is my first contribution, I hope have sent it to the right
>
> Best regards
>
> Philippe LALLOUET
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```