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 A231611 The least k such that the polynomial cyclotomic(k,x) has n different coefficients. 1

%I

%S 2,1,12,105,330,385,770,1365,1995,1785,3570,5610,2805,6279,3135,14245,

%T 13209,6545,7917,12903,17017,21385,22715,11165,22330,21505,29393,

%U 20930,10465,16555,31395,19285,38570,37961,35581,35105,52003,79373,18445,35245,23205,46345

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

%e 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.

%t 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

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

%K nonn,hard

%O 1,1

%A _T. D. Noe_, Dec 09 2013

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Last modified September 25 16:13 EDT 2020. Contains 337344 sequences. (Running on oeis4.)