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 A356896 #8 Sep 05 2022 05:24:46
%S A356896 0,2,3,4,6,9,10,11,13,14,15,16,17,19,22,23,24,26,28,30,33,34,35,37,38,
%T A356896 39,40,41,43,46,47,48,50,51,53,54,55,57,58,59,60,61,63,66,67,68,70,72,
%U A356896 74,77,78,79,81,82,83,84,85,87,90,91,92,94,96,97,98,100,103
%N A356896 Nonnegative numbers whose maximal tribonacci representation (A352103) ends in an even number of 1's.
%C A356896 Numbers k such that A356898(k) is even.
%C A356896 The asymptotic density of this sequence is c/(c+1) = 0.647798..., where c = 1.839286... (A058265) is the tribonacci constant.
%H A356896 Amiram Eldar, <a href="/A356896/b356896.txt">Table of n, a(n) for n = 1..10000</a>
%e A356896 n a(n) A352103(n) A356898(n)
%e A356896 - ---- ---------- ----------
%e A356896 1 0 0 0
%e A356896 2 2 10 0
%e A356896 3 3 11 2
%e A356896 4 4 100 0
%e A356896 5 6 110 0
%e A356896 6 9 1010 0
%e A356896 7 10 1011 2
%e A356896 8 11 1100 0
%e A356896 9 13 1110 0
%e A356896 10 14 1111 4
%t A356896 t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; trib[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; IntegerDigits[Total[2^(s - 1)], 2]]; f[v_] := Module[{m = Length[v], k}, k = m; While[v[[k]] == 1, k--]; m - k]; c[n_] := Module[{v = trib[n]}, nv = Length[v]; i = 1; While[i <= nv - 3, If[v[[i ;; i + 3]] == {1, 0, 0, 0}, v[[i ;; i + 3]] = {0, 1, 1, 1}; If[i > 3, i -= 4]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, 0, f[v[[i[[1, 1]] ;; -1]]], 10]]; Select[Range[0, 100], EvenQ[c[#]] &]
%Y A356896 Complement of A356897.
%Y A356896 Cf. A058265, A352103, A356898.
%Y A356896 Similar sequences: A308197, A342051.
%K A356896 nonn,base
%O A356896 1,2
%A A356896 _Amiram Eldar_, Sep 03 2022