[seqfan] Re: SeqFan Digest, Vol 95, Issue 1

[Peter Lawrence]

Jan Orwat,
           Many thanks,

as a software professional by day (and a mathematician only by night)
I can't believe I made such a rookie C programming mistake,
the C language "%" remainder operator is broken for negative dividends
and does not compute modulo arithmetic, after fixing this I get the
same numbers as you. The patterns in these numbers are much simpler.
Again, many thanks.

Peter Lawrence.



 >Dear Peter,
 >
 >For C30(x) I've got a row of all ones (mod 30).
 >Your result C30(1) -> 17, suggests you use other coefficients than  
[ 1, 1,
 >0,-1,-1,-1, 0, 1, 1].
 >Check if C30(x) equals C15(-x).
 >
 >Best regards,
 >Jan Orwat
 >
 >2016-08-05 7:20 GMT+02:00 Peter Lawrence <peterl95124 at  
sbcglobal.net>:
 >
 >>
 >> I was playing around with cyclotomic polynomials,
 >> in particular I was wondering how to verify my calculations
 >> of their coefficients without using floating-point arithmetic
 >> to evaluate their supposed roots
 >>
 >> and wondered about the values of Cn(x) modulo n
 >> evaluated for x in 0..n-1,
 >>
 >> I did not seem to find these values in OEIS,
 >> did I compute them incorrectly ?
 >>
 >> there are some obvious patterns in the numbers I computed with  
modulo n
 >> arithmetic
 >> Cp(x) ---> 1,0,1,1,1,1,.....
 >> Cp^e(x) :  all 1's except Cn(1), Cn(1+p), Cn(1+2p), ..., Cn(1+p^e- 
p) ---> p
 >> Cn(x) with n = 2q with q odd:  Cn(q-1), Cn(2q-1) ---> q
 >>
 >> but things seem to get wild around C30(x),
 >>
 >> would anyone else like to verify the triangle of values I came up  
with
 >> for n = 1,..., 30  ?
 >>    1
 >>    1  0
 >>    1  0  1
 >>    1  2  1  2
 >>    1  0  1  1  1
 >>    1  1  3  1  1  3
 >>    1  0  1  1  1  1  1
 >>    1  2  1  2  1  2  1  2
 >>    1  3  1  1  3  1  1  3  1
 >>    1  1  1  1  5  1  1  1  1  5
 >>    1  0  1  1  1  1  1  1  1  1  1
 >>    1  1  1  1  1  1  1  1  1  1  1  1
 >>    1  0  1  1  1  1  1  1  1  1  1  1  1
 >>    1  1  1  1  1  1  7  1  1  1  1  1  1  7
 >>    1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 >>    1  2  1  2  1  2  1  2  1  2  1  2  1  2  1  2
 >>    1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 >>    1  1  3  1  1  3  1  1  3  1  1  3  1  1  3  1  1  3
 >>    1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 >>    1  1  5  5  1  1  1  5  5  1  1  1  5  5  1  1  1  5  5  1
 >>    1  1  7  1  7  1  1  1  1  7  1  7  1  1  1  1  7  1  7  1  1
 >>    1  1  1  1  1  1  1  1  1  1 11  1  1  1  1  1  1  1  1  1  1 11
 >>    1  0  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  1   
1  1  1
 >>    1  5  1  1  1  1  5  1  1  1  1  5  1  1  1  1  5  1  1  1  1   
5  1  1
 >> 1
 >>    1  1  1  1  1  1  1  1  1  1  1  1 13  1  1  1  1  1  1  1  1   
1  1  1
 >> 1 13
 >>    1  3  1  1  3  1  1  3  1  1  3  1  1  3  1  1  3  1  1  3  1   
1  3  1
 >> 1  3  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  0  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 17  1  1  1 21  1  1  1 25  1 27  1  1 15  1  1  1  1  5 21   
1  1  1
 >> 25  1  1  1  1 15
 >>
 >> if these values are correct I'll go ahead and submit the sequence,
 >> then see if I can prove the observations,
 >> but the last line above for 30 seems without pattern,
 >>
 >>
 >> thanks,
 >> Peter Lawrence.
 >>
 >>
 >>
 >> --