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
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