|
Search: id:A087482
|
|
|
| A087482 |
|
Number of binary polynomials of degree n irreducible over the integers. |
|
+0
3
|
|
| 2, 2, 2, 6, 8, 21, 34, 84, 150, 331, 614, 1417, 2638, 5508, 10874, 23437
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
A binary polynomial is defined as a monic polynomial whose remaining coefficients are either 0 or 1. For each n, there are 2^n polynomials to consider.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Irreducible Polynomial
|
|
MATHEMATICA
|
Irreducible[p_, n_] := Module[{f}, f=FactorList[p, Modulus->n]; Length[f]==1 || Simplify[p-f[[2, 1]]]===0]; Table[xx=x^Range[0, n-1]; cnt=0; Do[p=x^n+xx.(IntegerDigits[i, 2, n]); If[Irreducible[p, 0], cnt++ ], {i, 0, 2^n-1}]; cnt, {n, 16}]
|
|
CROSSREFS
|
Cf. A087481 (irreducible polynomials of the form x^n +- x^(n-1) +- x^(n-2) +- ... +- 1).
Sequence in context: A105341 A151694 A121698 this_sequence A137227 A052537 A024945
Adjacent sequences: A087479 A087480 A087481 this_sequence A087483 A087484 A087485
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Sep 09 2003
|
|
|
Search completed in 0.002 seconds
|
