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Orders of cyclotomic polynomials containing a coefficient the absolute value of which is >= 4.
0

%I #28 Nov 28 2016 05:02:57

%S 1365,1785,1995,2145,2415,2431,2717,2730,2737,2805,2849,3003,3135,

%T 3255,3315,3553,3570,3689,3705,3795,3885,3927,3990,4081,4095,4147,

%U 4199,4290,4305,4485,4515,4543,4641,4785,4830,4845,4862,4991,5005,5115,5187,5291,5313

%N Orders of cyclotomic polynomials containing a coefficient the absolute value of which is >= 4.

%p isA013592 := proc(n)

%p numtheory[cyclotomic](n,x) ;

%p {coeffs(%,x)} ;

%p map(abs,%) ;

%p if % minus {1,2,3} = {} then

%p false;

%p else

%p true;

%p end if;

%p end proc:

%p for n from 1 do

%p if isA013592(n) then

%p print(n);

%p end if;

%p end do: # _R. J. Mathar_, Nov 28 2016

%t S[ n_ ] := For[ j=1; t=0, j<n, j++, t=Cases[ CoefficientList[ Cyclotomic[ j, x ], x ], k_ /; Abs[ k ]>3 ]; If[ Length[ t ]!=0, Print[ j ] ] ]; S[ 4290 ]

%t Select[Range[6300],Max[Abs[CoefficientList[Cyclotomic[#,x],x]]]>3&] (* _Harvey P. Dale_, Feb 26 2015 *)

%o (PARI) isok(n) = my(v = Vec(polcyclo(n))); (vecmax(v) >= 4) || (vecmin(v) <= -4); \\ _Michel Marcus_, Feb 26 2015

%K nonn

%O 1,1

%A Peter T. Wang (peterw(AT)cco.caltech.edu)

%E Definition clarified by and more terms from _Harvey P. Dale_, Feb 26 2015