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 A106449 #28 Oct 22 2019 04:23:28
%S A106449 0,3,3,2,0,2,5,1,1,5,4,3,0,3,4,7,7,7,7,7,7,6,2,2,0,2,2,6,9,5,3,1,1,3,
%T A106449 5,9,8,5,4,1,0,1,4,5,8,11,11,11,3,1,1,3,11,11,11,10,4,6,3,2,0,2,3,6,4,
%U A106449 10,13,9,7,13,13,1,1,13,13,7,9,13,12,7,8,7,4,7,0,7,4,7,8,7,12,15,15,5
%N A106449 Square array (P(x) XOR P(y))/gcd(P(x),P(y)) where P(x) and P(y) are polynomials with coefficients in {0,1} given by the binary expansions of x and y, and all calculations are done in polynomial ring GF(2)[X], with the result converted back to a binary number, and then expressed in decimal. Array is symmetric, and is read by antidiagonals.
%C A106449 Array is read by antidiagonals, with row x and column y ranging as: (x,y) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...
%C A106449 "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).
%C A106449 This is GF(2)[X] analog of A106448. In the definition XOR means addition in polynomial ring GF(2)[X], that is, a carryless binary addition, A003987.
%H A106449 Antti Karttunen, <a href="/A106449/b106449.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%H A106449 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A106449 A(x, y) = A280500(A003987(x, y), A091255(x, y)), that is, A003987(x, y) = A048720(A(x, y), A091255(x, y)).
%e A106449 The top left 17 X 17 corner of the array:
%e A106449 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
%e A106449 +--------------------------------------------------------------------
%e A106449 1 : 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, ...
%e A106449 2 : 3, 0, 1, 3, 7, 2, 5, 5, 11, 4, 9, 7, 15, 6, 13, 9, 19, ...
%e A106449 3 : 2, 1, 0, 7, 2, 3, 4, 11, 6, 7, 8, 5, 14, 13, 4, 19, 14, ...
%e A106449 4 : 5, 3, 7, 0, 1, 1, 3, 3, 13, 7, 15, 2, 9, 5, 11, 5, 21, ...
%e A106449 5 : 4, 7, 2, 1, 0, 1, 2, 13, 4, 3, 14, 7, 8, 11, 2, 21, 4, ...
%e A106449 6 : 7, 2, 3, 1, 1, 0, 1, 7, 5, 2, 13, 3, 11, 4, 7, 11, 13, ...
%e A106449 7 : 6, 5, 4, 3, 2, 1, 0, 15, 2, 13, 12, 11, 10, 3, 8, 23, 22, ...
%e A106449 8 : 9, 5, 11, 3, 13, 7, 15, 0, 1, 1, 3, 1, 5, 3, 7, 3, 25, ...
%e A106449 9 : 8, 11, 6, 13, 4, 5, 2, 1, 0, 1, 2, 3, 4, 1, 2, 25, 8, ...
%e A106449 10 : 11, 4, 7, 7, 3, 2, 13, 1, 1, 0, 1, 1, 7, 2, 1, 13, 7, ...
%e A106449 11 : 10, 9, 8, 15, 14, 13, 12, 3, 2, 1, 0, 7, 6, 5, 4, 27, 26, ...
%e A106449 12 : 13, 7, 5, 2, 7, 3, 11, 1, 3, 1, 7, 0, 1, 1, 1, 7, 11, ...
%e A106449 13 : 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2, 29, 28, ...
%e A106449 14 : 15, 6, 13, 5, 11, 4, 3, 3, 1, 2, 5, 1, 3, 0, 1, 15, 31, ...
%e A106449 15 : 14, 13, 4, 11, 2, 7, 8, 7, 2, 1, 4, 1, 2, 1, 0, 31, 2, ...
%e A106449 16 : 17, 9, 19, 5 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 0, 1, ...
%e A106449 17 : 16, 19, 14, 21, 4, 13, 22, 25, 8, 7, 26, 11, 28, 31, 2, 1, 0, ...
%o A106449 (PARI)
%o A106449 up_to = 105;
%o A106449 A106449sq(a,b) = { my(Pa=Pol(binary(a))*Mod(1, 2), Pb=Pol(binary(b))*Mod(1, 2)); fromdigits(Vec(lift((Pa+Pb)/gcd(Pa,Pb))),2); }; \\ Note that XOR is just + in GF(2)[X] world.
%o A106449 A106449list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A106449sq(col,(a-(col-1))))); (v); };
%o A106449 v106449 = A106449list(up_to);
%o A106449 A106449(n) = v106449[n]; \\ _Antti Karttunen_, Oct 21 2019
%Y A106449 Row 1: A004442 (without its initial term), row 2: A106450 (without its initial term).
%Y A106449 Cf. A003987, A048720, A091255, A106448, A280500.
%K A106449 nonn,tabl
%O A106449 1,2
%A A106449 _Antti Karttunen_, May 21 2005