A231611 The least k such that the polynomial cyclotomic(k,x) has n different coefficients.

2, 1, 12, 105, 330, 385, 770, 1365, 1995, 1785, 3570, 5610, 2805, 6279, 3135, 14245, 13209, 6545, 7917, 12903, 17017, 21385, 22715, 11165, 22330, 21505, 29393, 20930, 10465, 16555, 31395, 19285, 38570, 37961, 35581, 35105, 52003, 79373, 18445, 35245, 23205, 46345

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

The polynomial cyclotomic(2,x) is x + 1, which has both coefficients equal to 1. Hence, a(1) = 2. The polynomial cyclotomic(1,x) is x - 1, which has two coefficients 1 and -1. Hence, a(2) = 1. The polynomial cyclotomic(12,x) is x^4 + 0*x^3 - x^2 + 0*x + 1, which has coefficients -1, 0, and 1. This is the first cyclotomic polynomial having 3 different coefficients. Hence a(3) = 12.

Mathematica

nn = 10; t = Table[0, {nn}]; k = 0; found = 0; While[found < nn, k++; len = Length[Union[CoefficientList[Cyclotomic[k, x], x]]]; If[len <= nn && t[[len]] == 0, t[[len]] = k; found++]]; t

Crossrefs

Cf. A230798 (number of distinct coefficients in cyclotomic(n,x)).

Sequence in context: A053566 A009483 A181867 * A171510 A106750 A258821

Adjacent sequences: A231608 A231609 A231610 * A231612 A231613 A231614

Keyword

nonn,hard

Author

T. D. Noe, Dec 09 2013

Status

approved