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 A365618 #55 Jan 20 2024 09:11:12
%S A365618 0,1,1,1,2,1,2,2,2,2,1,3,2,3,1,2,2,3,3,2,2,2,3,2,4,2,3,2,3,3,3,3,3,3,
%T A365618 3,3,1,4,3,4,2,4,3,4,1,2,2,4,4,3,3,4,4,2,2,2,3,2,5,3,4,3,5,2,3,2,3,3,
%U A365618 3,3,4,4,4,4,3,3,3,3,2,4,3,4,2,5,4,5,2
%N A365618 Table read by antidiagonals: T(n, k) = A000120(n) + A000120(k).
%C A365618 T(n, k) is the sum of the Hamming weight of n and the Hamming weight of k.
%C A365618 Picking all points (n, k) such that T(n, k) <= N for some natural number N iteratively generates a Sierpinski-like fractal H. To generate the fractal, fix i and produce the set H_i = {(x, y) in [0, 1)^2 : T(floor(x * 2^i), floor(y * 2^i)) <= i}. Then, define the "limit fractal" H = {(x, y) in [0, 1)^2 : there exists N such that (x, y) is in H_i for all i >= N}.
%C A365618 The table is symmetric, T(n, k) = T(k, n).
%C A365618 See A367055 for a triangle read by rows.
%H A365618 Mithra Karamchedu, <a href="/A365618/a365618.png">Points (n, k), indicated in black, where T(n, k) <= 12, 0 <= n, k < 2^12</a>.
%F A365618 T(n, k) = A000120(n) + A000120(k).
%F A365618 If n_1 and n_2 share no 1 bits in common, then T(n_1 + n_2, k) = A000120(n_1) + A000120(n_2) + A000120(k).
%e A365618 The table begins:
%e A365618 k=0 1 2 3 4
%e A365618 n=0: 0 1 1 2 1 ...
%e A365618 n=1: 1 2 2 3 2 ...
%e A365618 n=2: 1 2 2 3 2 ...
%e A365618 n=3: 2 3 3 4 3 ...
%e A365618 n=4: 1 2 2 3 2 ...
%t A365618 T[n_, k_] := DigitCount[n, 2, 1] + DigitCount[k, 2, 1]
%Y A365618 Cf. A000120, A367055.
%K A365618 nonn,tabl,base,easy
%O A365618 0,5
%A A365618 _Mithra Karamchedu_ and _Sophia Pi_, Nov 03 2023