|
|
A087653
|
|
Maximum difference between exponents in n-th cyclotomic polynomial.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(p) = a(p*q) = p-1 for primes p < q (by Hong et al.). - Jonathan Sondow, Jan 09 2014
|
|
EXAMPLE
|
Cyc(9) = x^6 + x^3 + x^0, so a(9) = 3.
|
|
MATHEMATICA
|
a[n_] := Max[Differences[Exponent[Cyclotomic [n, x], x, List]]] (* Jonathan Sondow, Jan 09 2014 *)
|
|
PROG
|
(PARI) { mtermgap(pol)=local(p, m); m=0; p=0; for(k=0, poldegree(pol), if(polcoeff(pol, k)!=0, if(m<p, m=p); p=0, p=p+1)); max(m, p)+1 }
for(n=1, 200, print1(mtermgap(polcyclo(n))", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|