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 A091242 #32 Jan 04 2022 04:08:56
%S A091242 4,5,6,8,9,10,12,14,15,16,17,18,20,21,22,23,24,26,27,28,29,30,32,33,
%T A091242 34,35,36,38,39,40,42,43,44,45,46,48,49,50,51,52,53,54,56,57,58,60,62,
%U A091242 63,64,65,66,68,69,70,71,72,74,75,76,77,78,79,80,81,82,83,84,85,86,88
%N A091242 Reducible polynomials over GF(2), coded in binary.
%C A091242 "Coded in binary" means that a polynomial a(n)*X^n+...+a(0)*X^0 over GF(2) is represented by the binary number a(n)*2^n+...+a(0)*2^0 in Z (where a(k)=0 or 1). - _M. F. Hasler_, Aug 18 2014
%C A091242 The reducible polynomials in GF(2)[X] are the analog to the composite numbers A002808 in the integers.
%C A091242 It follows that the sequence is closed under application of A048720(.,.), which effects multiplication of the coded polynomials. It is also closed under application of blue code, A193231. The majority of the terms are coded multiples of X^1 (represented by 2) and/or X^1+1 (represented by 3): see A005843 and A001969 respectively. A246157 lists the other terms. - _Peter Munn_, Apr 20 2021
%H A091242 Robert Israel, <a href="/A091242/b091242.txt">Table of n, a(n) for n = 1..10000</a>
%H A091242 Antti Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>
%H A091242 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e A091242 For example, 5 = 101 in binary encodes the polynomial x^2+1 which is factored as (x+1)^2 in the polynomial ring GF(2)[X].
%p A091242 filter:= proc(n) local L;
%p A091242 L:= convert(n,base,2);
%p A091242 not Irreduc(add(L[i]*x^(i-1),i=1..nops(L))) mod 2
%p A091242 end proc:
%p A091242 select(filter, [$2..200]); # _Robert Israel_, Aug 30 2018
%t A091242 okQ[n_] := Module[{x, id = IntegerDigits[n, 2] // Reverse}, !IrreduciblePolynomialQ[id.x^Range[0, Length[id]-1], Modulus -> 2]];
%t A091242 Select[Range[2, 200], okQ] (* _Jean-François Alcover_, Jan 04 2022 *)
%Y A091242 Inverse: A091246. Almost complement of A014580. Union of A091209 & A091212. First differences: A091243. Characteristic function: A091247. In binary format: A091254.
%Y A091242 Number of degree-n reducible polynomials: A058766.
%Y A091242 Subsequences: A001969\{0,3}, A005843\{0,2}, A246156, A246157, A246158, A316970.
%Y A091242 Cf. A002808, A048720, A193231.
%K A091242 nonn
%O A091242 1,1
%A A091242 _Antti Karttunen_, Jan 03 2004
%E A091242 Edited by _M. F. Hasler_, Aug 18 2014