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A137979 Highest coefficient occurring in the factorization of x^n - 1 over the reals. 4
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,105
COMMENTS
Based on a comment in Mathematica helpfile ref/Factor - Neat Examples.
The first factorization of x^n - 1 in which a 2 appears as a coefficient is for n=105.
Different from A160338, see comment there.
LINKS
EXAMPLE
a(4) = 1 because x^4 - 1 = (x^2+1)(x+1)(x-1) and the highest coefficient of these three terms is 1.
The first time a 2 appears is at n=105, where the factorization is:
(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*
(x^24-x^23+x^19-x^18+x^17-x^16+x^14-x^13+x^12-x^11+x^10-x^8+x^7-x^6+x^5-x+1)*
(x^2+x+1)*(x^12-x^11+x^9-x^8+x^6-x^4+x^3-x+1)*
(x^8-x^7+x^5-x^4+x^3-x+1)*
(x^48+x^47+x^46-x^43-x^42-2*x^41-x^40-x^39+x^36+x^35+x^34+x^33+x^32+x^31-x^28-x^26-x^24-x^22-x^20+x^17+x^16+x^15+x^14+x^13+x^12-x^9-x^8-2*x^7-x^6-x^5+x^2+x+1). - N. J. A. Sloane, Apr 18 2008
MATHEMATICA
Table[Max[Abs[Flatten[CoefficientList[Transpose[FactorList[x^i - 1]][[1]], x]]]], {i, 1, 1000}]
PROG
(PARI) a(n) = {my(f = factor(x^n-1)); vecmax(vector(#f~, k, vecmax(apply(x->abs(x), Vec(f[k, 1]))))); } \\ Michel Marcus, Dec 05 2018
CROSSREFS
Sequence in context: A084928 A112316 A112802 * A160338 A216579 A229878
KEYWORD
nonn
AUTHOR
Ian Miller, Feb 25 2008
STATUS
approved

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