|
Search: id:A105609
|
|
|
| A105609 |
|
Sylvester numbers for 1/(1+x^2). |
|
+0
3
|
|
| 1, 0, -1, -2, 1, -3, -1, 2, -1, 5, -1, 1, 1, -7, 1, 2, 1, -3, -1, 1, 1, -11, -1, 1, 1, 13, -1, 1, 1, 1, -1, 2, 1, 17, 1, 1, 1, -19, 1, 1
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number.
|
|
FORMULA
|
a(n)=product{k=1..n-1, if(gcd(n, k)=1, (I+I*exp(2*pi*I*k/n), 1)}, I=sqrt(-1)
|
|
EXAMPLE
|
(x+I)(x-I)=1+x^2
|
|
MATHEMATICA
|
f[n_] := FullSimplify[ Expand[Times @@ (I + I*Exp[2Pi*I*Select[Range[n], GCD[ #, n] == 1 &]/n])]]; Table[ f[n], {n, 0, 32}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 02 2005)
|
|
CROSSREFS
|
Cf. A020513, A105608, A105607.
Sequence in context: A065704 A026100 A059127 this_sequence A101872 A069929 A101312
Adjacent sequences: A105606 A105607 A105608 this_sequence A105610 A105611 A105612
|
|
KEYWORD
|
easy,sign,more
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Apr 15 2005
|
|
|
Search completed in 0.002 seconds
|
