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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

Differs from A000190, A003557, A073752.

LINKS

Michel Marcus, Table of n, a(n) for n = 1..5000

Hoon Hong, Eunjeong Lee, Hyang-Sook Lee, Cheol-Min Park, Maximum Gap in (Inverse) Cyclotomic Polynomial, arXiv:1101.4255 [math.NT], 2011.

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

Cf. A013595.

Sequence in context: A003557 A073752 A128708 * A295666 A322020 A294895

Adjacent sequences:  A087650 A087651 A087652 * A087654 A087655 A087656

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Sep 25 2003

STATUS

approved

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Last modified December 16 19:11 EST 2018. Contains 318188 sequences. (Running on oeis4.)