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A087482
Number of binary polynomials of degree n irreducible over the integers.
2
2, 2, 2, 6, 8, 21, 34, 84, 150, 331, 614, 1417, 2638, 5508, 10874, 23437, 44862, 95887, 185238, 390297, 765510, 1557427, 3043918, 6525948, 12706892, 25836122, 51135384, 105070336, 206266718, 426254492
OFFSET
1,1
COMMENTS
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
FORMULA
a(n) >= A001037(n). - Joerg Arndt, Dec 22 2014
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}]
PROG
(PARI) a(n)= { if( n<=2, return(2)); my(d, P, ct=0, x='x); forstep (k=1, 2^n-1, 2, P=x^n+Pol(binary(k), x); ct+=polisirreducible(P) ); return(ct); }
for(n=1, 30, print1(a(n), ", ")); \\ Joerg Arndt, Dec 22 2014
CROSSREFS
Cf. A087481 (irreducible polynomials of the form x^n +- x^(n-1) +- x^(n-2) +- ... +- 1).
Cf. A001037 (irreducible polynomials over GF(2)).
Sequence in context: A298745 A323860 A121698 * A137227 A323862 A291667
KEYWORD
nonn,more
AUTHOR
T. D. Noe, Sep 09 2003
EXTENSIONS
Added more terms, Joerg Arndt, Dec 22 2014
a(23)-a(30) from Max Alekseyev, May 07 2022
STATUS
approved