On the notion of "coefficient" (related to A046887).

Giovanni Resta g.resta at iit.cnr.it
Tue Jan 31 15:34:52 CET 2006


Dear seqfans,

I planned to extend the sequence A046887 
<http://www.research.att.com/%7Enjas/sequences/A046887> :

"Cyclotomic polynomial of order n has a coefficient which does not 
appear in any cyclotomic
polynomials of lower order."
Currently = 1, 105, 165, 385, 595, 1365, 1785, 2145, 2805, 3135, 6545, 7917.

So, I computed the values in the range 7918-30000 which are:

10465, 11305, 15015, 17255, 20615, 25935, 26565.

However, I have the following doubt on the notion of coefficient:
let us consider the 4th cyclotomic polynomial:

Cy(4)= x^2+1

According to my personal (and probably erroneous) notion of "coefficient",
the coefficients of Cy(4) are  1,0,1,  since Cy(4)=1*x^2+0*x+1*1

And, if 0 is considered a coefficient, then the sequence above is incorrect,
and should be:

1, 4, 105, 165, 385, ... instead of   1, 105, 165, 385,....

since 0 appears in Cy(4) and never before.

Can anybody clarify the matter for me, so that I can submit the right
comment/extension to OEIS ?

Thanks,
giovanni.








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