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

1,1

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

Links

Table of n, a(n) for n=1..46.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A065119, A086765.

Sequence in context: A088005 A340459 A125237 * A092169 A093108 A247519

Adjacent sequences: A085456 A085457 A085458 * A085460 A085461 A085462

Keyword

nonn,easy

Author

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

Extensions

More terms from David Wasserman, Feb 01 2005

Status

approved