This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A087482 #21 Feb 16 2025 08:32:51
%S A087482 2,2,2,6,8,21,34,84,150,331,614,1417,2638,5508,10874,23437,44862,
%T A087482 95887,185238,390297,765510,1557427,3043918,6525948,12706892,25836122,
%U A087482 51135384,105070336,206266718,426254492
%N A087482 Number of binary polynomials of degree n irreducible over the integers.
%C A087482 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.
%H A087482 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrreduciblePolynomial.html">Irreducible Polynomial</a>
%F A087482 a(n) >= A001037(n). - _Joerg Arndt_, Dec 22 2014
%t A087482 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}]
%o A087482 (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); }
%o A087482 for(n=1,30,print1(a(n),", ")); \\ _Joerg Arndt_, Dec 22 2014
%Y A087482 Cf. A087481 (irreducible polynomials of the form x^n +- x^(n-1) +- x^(n-2) +- ... +- 1).
%Y A087482 Cf. A001037 (irreducible polynomials over GF(2)).
%K A087482 nonn,more
%O A087482 1,1
%A A087482 _T. D. Noe_, Sep 09 2003
%E A087482 Added more terms, _Joerg Arndt_, Dec 22 2014
%E A087482 a(23)-a(30) from _Max Alekseyev_, May 07 2022