The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A095878 Value of middle coefficient of the cyclotomic polynomial Phi_n(x) for n in A095877. 1
 1, 0, -1, -3, 3, 5, -5, -7, 7, 19, -11, 25, 11, 27, -9, 9, 45, 13, -35, -15, -23, 17, 349, -65, -27, -17, 15, -13, 21, -21, -19, 165, -29, 23, -37, 91, 29, 37, 33, -63, 161, 69, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS After the second term, the entries are always odd; see Dresden's article for proof. LINKS G. Dresden, On the Middle Coefficient of a Cyclotomic Polynomial (MAA Monthly, 2004, 531-533). MAPLE vals:= {1, 0, -1}: a[1]:= 1; a[2]:= 0: a[3]:= -1: count:= 3: for n from 4 while count < 20 do f:= ifactors(n)[2]; if nops(f) <= 2 or max(f[.., 2])>1 then next fi; p:= numtheory:-cyclotomic(n, x); c:= coeff(p, x, degree(p, x)/2); if not member(c, vals) then count:= count+1; a[count]:= c; vals:= vals union {c}; fi od: seq(a[i], i=1..count); # Robert Israel, Dec 18 2014 MATHEMATICA vals={1, 0, -1}; lst={3, 4, 6}; Do[pwrs=Transpose[FactorInteger[n]][[2]]; If[Length[pwrs]>2 && 1==Times@@pwrs, c=Coefficient[Cyclotomic[n, x], x, EulerPhi[n]/2]; If[ !MemberQ[vals, c], AppendTo[lst, n]; AppendTo[vals, c]]], {n, 7, 50000, 2}]; vals CROSSREFS Cf. A094754 (middle coefficient of cyclotomic polynomial Phi_n(x)). Sequence in context: A333153 A245146 A339102 * A341143 A157966 A212597 Adjacent sequences: A095875 A095876 A095877 * A095879 A095880 A095881 KEYWORD hard,sign AUTHOR T. D. Noe, Jun 10 2004 EXTENSIONS More terms from Jozsef Pelikan, Dec 18 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 3 04:25 EST 2023. Contains 360024 sequences. (Running on oeis4.)