A087653 Maximum difference between exponents in n-th cyclotomic polynomial.
1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 2, 8, 1, 3, 1, 2, 2, 1, 1, 4, 5, 1, 9, 2, 1, 2, 1, 16, 2, 1, 4, 6, 1, 1, 2, 4, 1, 2, 1, 2, 6, 1, 1, 8, 7, 5, 2, 2, 1, 9, 4, 4, 2, 1, 1, 4, 1, 1, 6, 32, 4, 2, 1, 2, 2, 4, 1, 12, 1, 1, 10, 2, 6, 2, 1, 8, 27, 1, 1, 4, 4, 1, 2, 4, 1, 6, 6, 2, 2, 1, 4
Offset: 1
Examples
Cyc(9) = x^6 + x^3 + x^0, so a(9) = 3.
Links
- Michel Marcus, Table of n, a(n) for n = 1..5000
- Ala'a Al-Kateeb, Mary Ambrosino, Hoon Hong, and Eunjeong Lee, Maximum gap in cyclotomic polynomials, arXiv:1911.11667 [math.NT], 2019.
- Hoon Hong, Eunjeong Lee, Hyang-Sook Lee, Cheol-Min Park, Maximum Gap in (Inverse) Cyclotomic Polynomial, arXiv:1101.4255 [math.NT], 2011.
Crossrefs
Cf. A013595.
Programs
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Mathematica
a[n_] := Max[Differences[Exponent[Cyclotomic [n, x], x, List]]] (* Jonathan Sondow, Jan 09 2014 *)
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PARI
{ mtermgap(pol)=local(p, m); m=0; p=0; for(k=0, poldegree(pol), if(polcoeff(pol, k)!=0, if(m
Formula
a(p) = a(p*q) = p-1 for primes p < q (by Hong et al.). - Jonathan Sondow, Jan 09 2014
Comments