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A137979 Highest coefficient occuring 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.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

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}]

CROSSREFS

Cf. A013590, A013594.

Sequence in context: * A160338 A229878 A235145 A037281 A143241 A118626

Adjacent sequences:  A137976 A137977 A137978 * A137980 A137981 A137982

KEYWORD

nonn

AUTHOR

Ian Miller, Feb 25 2008

STATUS

approved

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Last modified August 27 23:36 EDT 2014. Contains 246151 sequences.