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A231611 The least k such that the polynomial cyclotomic(k,x) has n different coefficients. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
nonn,hard
AUTHOR
T. D. Noe, Dec 09 2013
STATUS
approved

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Last modified May 23 10:34 EDT 2024. Contains 372760 sequences. (Running on oeis4.)