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 A369311 #9 Jan 21 2024 09:38:05
%S A369311 0,0,0,0,1,0,0,0,1,0,0,1,1,1,0,0,0,0,2,1,0,0,1,1,3,2,1,0,0,0,0,0,3,2,
%T A369311 1,0,0,1,0,1,1,3,2,1,0,0,0,1,2,0,2,3,2,1,0,0,1,1,3,3,3,3,3,2,1,0,0,0,
%U A369311 0,0,2,0,2,4,3,2,1,0,0,1,0,1,2,1,1,5,4,3,2,1,0
%N A369311 Square array A(n, k), n >= 0, k > 0, read by upwards antidiagonals: P(A(n, k)) is the remainder of the polynomial long division of P(n) by P(k) (where P(m) denotes the polynomial over GF(2) whose coefficients are encoded in the binary expansion of the nonnegative integer m).
%C A369311 For any number m >= 0 with binary expansion Sum_{k >= 0} b_k * 2^k, P(m) = Sum_{k >= 0} b_k * X^k.
%H A369311 Rémy Sigrist, <a href="/A369311/a369311.png">Colored scatterplot of (n, k) for n, k < 2^10</a> (where the color is function of A(n, k))
%H A369311 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e A369311 Array A(n, k) begins:
%e A369311 n\k | 1 2 3 4 5 6 7 8 9 10 11 12
%e A369311 ----+--------------------------------------
%e A369311 0 | 0 0 0 0 0 0 0 0 0 0 0 0
%e A369311 1 | 0 1 1 1 1 1 1 1 1 1 1 1
%e A369311 2 | 0 0 1 2 2 2 2 2 2 2 2 2
%e A369311 3 | 0 1 0 3 3 3 3 3 3 3 3 3
%e A369311 4 | 0 0 1 0 1 2 3 4 4 4 4 4
%e A369311 5 | 0 1 0 1 0 3 2 5 5 5 5 5
%e A369311 6 | 0 0 0 2 3 0 1 6 6 6 6 6
%e A369311 7 | 0 1 1 3 2 1 0 7 7 7 7 7
%e A369311 8 | 0 0 1 0 2 2 1 0 1 2 3 4
%e A369311 9 | 0 1 0 1 3 3 0 1 0 3 2 5
%e A369311 10 | 0 0 0 2 0 0 3 2 3 0 1 6
%e A369311 11 | 0 1 1 3 1 1 2 3 2 1 0 7
%e A369311 12 | 0 0 0 0 3 0 2 4 5 6 7 0
%o A369311 (PARI) A(n, k) = { fromdigits(lift(Vec( (Mod(1, 2) * Pol(binary(n))) % (Mod(1, 2) * Pol(binary(k))))), 2) }
%Y A369311 See A369312 for the corresponding quotients.
%Y A369311 Cf. A048158, A048720.
%K A369311 nonn,base,tabl
%O A369311 0,19
%A A369311 _Rémy Sigrist_, Jan 19 2024