A085459 Numbers k such that k-th cyclotomic polynomial has exactly 3 positive coefficients.

3, 9, 10, 20, 27, 40, 50, 80, 81, 100, 160, 200, 243, 250, 320, 400, 500, 640, 729, 800, 1000, 1250, 1280, 1600, 2000, 2187, 2500, 2560, 3200, 4000, 5000, 5120, 6250, 6400, 6561, 8000, 10000, 10240, 12500, 12800, 16000, 19683, 20000, 20480, 25000, 25600

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 14 2003

Keywords

• nonn
• easy

Comments

Sequence appears to consist of 3^i, i > 0; and 2^i*5^j, i, j > 0. Are there any other terms? - David Wasserman, Feb 01 2005

Examples

			9 is a member because the 9th cyclotomic polynomial is P(x) = x^6+x^3+1.
		

Crossrefs

Cf. A065119, A086765.

Programs

Mathematica

Select[Range@ 5000, Count[CoefficientList[Cyclotomic[#, x], x], ?(# > 0 &)] == 3 &] (* _Michael De Vlieger, Oct 26 2017 *)

PARI

n = 0; while (1, n++; p = polcyclo(n, x); d = poldegree(p); c = 0; i = 0; while (c < 4 && i <= d, if (polcoeff(p, i) > 0, c++); i++); if (c == 3, print(n))); \\ David Wasserman, Feb 01 2005

Extensions

More terms from David Wasserman, Feb 01 2005