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

Author

Antti Karttunen, Aug 03 2001

Keywords

• nonn
• base
• nice

Comments

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

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n=0..300
• Index entries for cyclotomic polynomials, positions of coefficients

Crossrefs

Cf. A063672, A063697, A063699.

Cf. A013595.

Programs

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 *)

Formula

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