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

0,1

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 1<n<20 except {11,12,15} and whenever A005420(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

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 *)

Prog

(PARI) A063670(n)=local(p=polcyclo(n+!n)); if(n, sum(i=0, n, (polcoeff(p, i)<>0)<<i), 2) \\ M. F. Hasler, Apr 30 2007
(PARI) a(n) = subst(apply(x->x!=0, polcyclo(n, 'x)), 'x, 2);  \\ Gheorghe Coserea, Nov 04 2016

Crossrefs

Cf. A013594.

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

This sequence in binary: A063671.

Cf. A005420.

Sequence in context: A076557 A228548 A140407 * A253357 A185909 A347533

Adjacent sequences: A063667 A063668 A063669 * A063671 A063672 A063673

Keyword

nonn,base

Author

Antti Karttunen, Aug 03 2001

Status

approved