|
Search: id:A137979
|
|
|
| A137979 |
|
Highest coefficient occuring in the factorization of x^n - 1 over the reals. |
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
1,105
|
|
|
COMMENT
|
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 coefficent 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). - njas, 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: A097516 A112802 A118269 this_sequence A037281 A118626 A062892
Adjacent sequences: A137976 A137977 A137978 this_sequence A137980 A137981 A137982
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ian Miller (ianxmiller(AT)gmail.com), Feb 25 2008
|
|
|
Search completed in 0.002 seconds
|
