A063670 Positions of nonzero coefficients in cyclotomic polynomial Phi_n(x), converted from binary to decimal.

2, 3, 3, 7, 5, 31, 7, 127, 17, 73, 31, 2047, 21, 8191, 127, 443, 257, 131071, 73, 524287, 341, 7003, 2047, 8388607, 273, 1082401, 8191, 262657, 5461, 536870911, 443, 2147483647, 65537, 1797851, 131071, 26181091, 4161, 137438953471, 524287

Offset: 0

Author

Antti Karttunen, Aug 03 2001

Keywords

• nonn
• base

Comments

a(n) = 2^n-1 whenever n is prime. It seems as if a(n) >= A005420(n) for all n (checked up to 200), with equality for all 1A005420(n)=2^n-1 (i.e., 2^n-1 is prime). - M. F. Hasler, Apr 30 2007

a(0) could also be 1. - T. D. Noe, Oct 29 2007

Links

• M. F. Hasler, Table of n, a(n) for n = 0..1000
• Index entries for cyclotomic polynomials, positions of coefficients

Crossrefs

Cf. A013594.

a(n) = A063696(n) (the positive terms) + A063698(n) (the negative terms).

This sequence in binary: A063671.

Cf. A005420.

Programs

Maple

[seq(Phi_pos_terms(j,2)+Phi_neg_terms(j,2),j=0..104)];

Mathematica

a[n_] := FromDigits[ If[# != 0, 1, 0]& /@ CoefficientList[ Cyclotomic[n, x], x], 2]; a[0] = 2; Table[a[n], {n, 0, 38}] (* Jean-François Alcover, Dec 11 2012 *)

PARI

A063670(n)=local(p=polcyclo(n+!n)); if(n,sum(i=0, n, (polcoeff(p, i)<>0)<M. F. Hasler, Apr 30 2007

PARI

a(n) = subst(apply(x->x!=0, polcyclo(n,'x)), 'x, 2);  \\ Gheorghe Coserea, Nov 04 2016