A063671 Positions of nonzero coefficients in cyclotomic polynomial Phi_n(x), A063670 in binary.

10, 11, 11, 111, 101, 11111, 111, 1111111, 10001, 1001001, 11111, 11111111111, 10101, 1111111111111, 1111111, 110111011, 100000001, 11111111111111111, 1001001, 1111111111111111111, 101010101, 1101101011011, 11111111111

Offset

0,1

Comments

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

Links

T. D. Noe, Table of n, a(n) for n=0..300

Index entries for cyclotomic polynomials, positions of coefficients

Formula

a(n) = A063697(n) (the positive terms) + A063699(n) (the negative terms) (computed in any base, up to n=104).

Example

Phi_15(x) = x^8 - x^7 + x^5 - x^4 + x^3 - x + 1, thus the 1-bits of a(15) are at positions 0,1,3,4,5,7 and 8, thus we get a(15) = 110111011.

Maple

map(convert, A063670, binary);

Mathematica

a[n_] := FromDigits[Abs[CoefficientList[Cyclotomic[n, x], x]]]; a[0]=10; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Nov 02 2016 *)

Crossrefs

Cf. A063672, A063697, A063699.

Cf. A013595.

Sequence in context: A008947 A108787 A097585 * A330024 A184992 A162501

Adjacent sequences: A063668 A063669 A063670 * A063672 A063673 A063674

Keyword

nonn,base,nice

Author

Antti Karttunen, Aug 03 2001

Status

approved