# [seqfan] An arithmetic sequence as zeros to polynomials.

Mats Granvik mgranvik at abo.fi
Sun Jul 22 09:55:35 CEST 2012

```The prime numbers are visible as zeros in this plot:

http://mobiusfunction.files.wordpress.com/2012/07/prime-polynomial.png

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, \
67, 71, 73, 79, 83, 89, 97}

The polynomial gives some other number as zeros also,
but they are relatively small.

I put the polynomials from 1 to 100
at pastebin:

http://pastebin.com/9eRkHcdz

What I would like to do is make a characteristic
sequence like this:

1,-1,1,1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,1,
1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,
1,1,1,1,-1,...

and take the Fourier transform of it and see
what the frequency spectrum looks like.

I made this sequence with this Excel formula:
=IF(J2=ROW();-L1;L1)

where J2 is the sequence:
1,2,3,1,5,1,7,1,1,1,11,1,13,1,1,1,17,...

But I have yet to find how to make it in Mathematica.

Dipl.Ing. Mats Granvik
Profil: http://math.stackexchange.com/users/8530/mats-granvik

```