A146960 Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) is not coefficient convex.

7735, 11305, 13845, 17255, 20615, 21945, 22015, 23919, 25935, 26565, 28595, 31535, 33495, 33915, 35105, 35805, 36465, 39767, 39865, 40755, 41041, 41055, 42315, 42665, 42735, 45885, 46189, 46655, 47355, 47957, 49665, 50505, 51051, 51765

Offset

1,1

Comments

Gallot and Moree say that a cyclotomic polynomial is coefficient convex if the union of the coefficients is a range of consecutive integers. They prove that if n is ternary (the product of three distinct odd primes), then Phi(n,x) is coefficient convex. All numbers in this sequence have more than three odd prime factors.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Yves Gallot and Pieter Moree, Neighboring ternary cyclotomic coefficients differ by at most one, arXiv:0810.5496 [math.NT], 2008.

Mathematica

nn = Select[Range[1155, 59999, 2], SquareFreeQ[#] && PrimeNu[#] > 3&];
Reap[For[k = 1, k <= Length[nn], k++, n = nn[[k]]; If[{1} != (CoefficientList[Cyclotomic[n, x], x] // Union // Differences // Union), Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 11 2018 *)

Crossrefs

Subsequence of A056911 (odd squarefree numbers).

Sequence in context: A202597 A092004 A278019 * A179574 A229419 A116239

Adjacent sequences: A146957 A146958 A146959 * A146961 A146962 A146963

Keyword

nonn

Author

T. D. Noe, Nov 03 2008

Extensions

Definition corrected by T. D. Noe, Nov 16 2008

Status

approved